Basic Math Examples

$(2 x + \frac{2}{3 y}) (3 x - \frac{3}{4 y}) = 6$

Step 1

Simplify $(2 x + \frac{2}{3 y}) (3 x - \frac{3}{4 y})$ .

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Step 1.1

Expand $(2 x + \frac{2}{3 y}) (3 x - \frac{3}{4 y})$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$2 x (3 x - \frac{3}{4 y}) + \frac{2}{3 y} (3 x - \frac{3}{4 y}) = 6$

Step 1.1.2

Apply the distributive property.

$2 x (3 x) + 2 x (- \frac{3}{4 y}) + \frac{2}{3 y} (3 x - \frac{3}{4 y}) = 6$

Step 1.1.3

Apply the distributive property.

$2 x (3 x) + 2 x (- \frac{3}{4 y}) + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x (- \frac{3}{4 y}) + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.1.2.1

Move $x$ .

$2 \cdot 3 (x \cdot x) + 2 x (- \frac{3}{4 y}) + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} + 2 x (- \frac{3}{4 y}) + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.3

Multiply $2$ by $3$ .

$6 x^{2} + 2 x (- \frac{3}{4 y}) + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.4

Cancel the common factor of $2$ .

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Step 1.2.1.4.1

Move the leading negative in $- \frac{3}{4 y}$ into the numerator.

$6 x^{2} + 2 x \frac{- 3}{4 y} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.4.2

Factor $2$ out of $2 x$ .

$6 x^{2} + 2 (x) \frac{- 3}{4 y} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.4.3

Factor $2$ out of $4 y$ .

$6 x^{2} + 2 (x) \frac{- 3}{2 (2 y)} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.4.4

Cancel the common factor.

$6 x^{2} + 2 x \frac{- 3}{2 (2 y)} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.4.5

Rewrite the expression.

$6 x^{2} + x \frac{- 3}{2 y} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.5

Combine $x$ and $\frac{- 3}{2 y}$ .

$6 x^{2} + \frac{x \cdot - 3}{2 y} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.6

Move $- 3$ to the left of $x$ .

$6 x^{2} + \frac{- 3 \cdot x}{2 y} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.7

Move the negative in front of the fraction.

$6 x^{2} - \frac{3 \cdot x}{2 y} + \frac{2}{3 y} (3 x) + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.8

Rewrite using the commutative property of multiplication.

$6 x^{2} - \frac{3 x}{2 y} + 3 \frac{2}{3 y} x + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.9

Cancel the common factor of $3$ .

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Step 1.2.1.9.1

Factor $3$ out of $3 y$ .

$6 x^{2} - \frac{3 x}{2 y} + 3 \frac{2}{3 (y)} x + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.9.2

Cancel the common factor.

$6 x^{2} - \frac{3 x}{2 y} + 3 \frac{2}{3 y} x + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.9.3

Rewrite the expression.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2}{y} x + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.10

Combine $\frac{2}{y}$ and $x$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{2}{3 y} (- \frac{3}{4 y}) = 6$

Step 1.2.1.11

Rewrite using the commutative property of multiplication.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} - \frac{2}{3 y} \cdot \frac{3}{4 y} = 6$

Step 1.2.1.12

Cancel the common factor of $2$ .

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Step 1.2.1.12.1

Move the leading negative in $- \frac{2}{3 y}$ into the numerator.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 2}{3 y} \cdot \frac{3}{4 y} = 6$

Step 1.2.1.12.2

Factor $2$ out of $- 2$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{2 (- 1)}{3 y} \cdot \frac{3}{4 y} = 6$

Step 1.2.1.12.3

Factor $2$ out of $4 y$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{2 (- 1)}{3 y} \cdot \frac{3}{2 (2 y)} = 6$

Step 1.2.1.12.4

Cancel the common factor.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{2 \cdot - 1}{3 y} \cdot \frac{3}{2 (2 y)} = 6$

Step 1.2.1.12.5

Rewrite the expression.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{3 y} \cdot \frac{3}{2 y} = 6$

Step 1.2.1.13

Cancel the common factor of $3$ .

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Step 1.2.1.13.1

Factor $3$ out of $3 y$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{3 (y)} \cdot \frac{3}{2 y} = 6$

Step 1.2.1.13.2

Cancel the common factor.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{3 y} \cdot \frac{3}{2 y} = 6$

Step 1.2.1.13.3

Rewrite the expression.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{y} \cdot \frac{1}{2 y} = 6$

Step 1.2.1.14

Multiply $\frac{- 1}{y}$ by $\frac{1}{2 y}$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{y (2 y)} = 6$

Step 1.2.1.15

Raise $y$ to the power of $1$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{2 (y^{1} y)} = 6$

Step 1.2.1.16

Raise $y$ to the power of $1$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{2 (y^{1} y^{1})} = 6$

Step 1.2.1.17

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{2 y^{1 + 1}} = 6$

Step 1.2.1.18

Add $1$ and $1$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} + \frac{- 1}{2 y^{2}} = 6$

Step 1.2.1.19

Move the negative in front of the fraction.

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.2

To write $\frac{2 x}{y}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x}{y} \cdot \frac{2}{2} - \frac{1}{2 y^{2}} = 6$

Step 1.2.3

Write each expression with a common denominator of $2 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.3.1

Multiply $\frac{2 x}{y}$ by $\frac{2}{2}$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x \cdot 2}{y \cdot 2} - \frac{1}{2 y^{2}} = 6$

Step 1.2.3.2

Reorder the factors of $y \cdot 2$ .

$6 x^{2} - \frac{3 x}{2 y} + \frac{2 x \cdot 2}{2 y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.4

Combine the numerators over the common denominator.

$6 x^{2} + \frac{- 3 x + 2 x \cdot 2}{2 y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.5

To write $6 x^{2}$ as a fraction with a common denominator, multiply by $\frac{2 y}{2 y}$ .

$6 x^{2} \cdot \frac{2 y}{2 y} + \frac{- 3 x + 2 x \cdot 2}{2 y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.6

Combine $6 x^{2}$ and $\frac{2 y}{2 y}$ .

$\frac{6 x^{2} (2 y)}{2 y} + \frac{- 3 x + 2 x \cdot 2}{2 y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.7

Combine the numerators over the common denominator.

$\frac{6 x^{2} (2 y) - 3 x + 2 x \cdot 2}{2 y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.8

To write $\frac{6 x^{2} (2 y) - 3 x + 2 x \cdot 2}{2 y}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{6 x^{2} (2 y) - 3 x + 2 x \cdot 2}{2 y} \cdot \frac{y}{y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.9

Write each expression with a common denominator of $2 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.9.1

Multiply $\frac{6 x^{2} (2 y) - 3 x + 2 x \cdot 2}{2 y}$ by $\frac{y}{y}$ .

$\frac{(6 x^{2} (2 y) - 3 x + 2 x \cdot 2) y}{2 y \cdot y} - \frac{1}{2 y^{2}} = 6$

Step 1.2.9.2

Multiply $y$ by $y$ by adding the exponents.

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Step 1.2.9.2.1

Move $y$ .

$\frac{(6 x^{2} (2 y) - 3 x + 2 x \cdot 2) y}{2 (y \cdot y)} - \frac{1}{2 y^{2}} = 6$

Step 1.2.9.2.2

Multiply $y$ by $y$ .

$\frac{(6 x^{2} (2 y) - 3 x + 2 x \cdot 2) y}{2 y^{2}} - \frac{1}{2 y^{2}} = 6$

Step 1.2.10

Combine the numerators over the common denominator.

$\frac{(6 x^{2} (2 y) - 3 x + 2 x \cdot 2) y - 1}{2 y^{2}} = 6$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $2$ by $6$ .

$\frac{(12 x^{2} y - 3 x + 2 x \cdot 2) y - 1}{2 y^{2}} = 6$

Step 1.3.1.2

Multiply $2$ by $2$ .

$\frac{(12 x^{2} y - 3 x + 4 x) y - 1}{2 y^{2}} = 6$

Step 1.3.2

Add $- 3 x$ and $4 x$ .

$\frac{(12 x^{2} y + x) y - 1}{2 y^{2}} = 6$

Step 1.3.3

Apply the distributive property.

$\frac{12 x^{2} y \cdot y + x y - 1}{2 y^{2}} = 6$

Step 1.3.4

Multiply $y$ by $y$ by adding the exponents.

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Step 1.3.4.1

Move $y$ .

$\frac{12 x^{2} (y \cdot y) + x y - 1}{2 y^{2}} = 6$

Step 1.3.4.2

Multiply $y$ by $y$ .

$\frac{12 x^{2} y^{2} + x y - 1}{2 y^{2}} = 6$

Step 1.3.5

Rewrite $12 x^{2} y^{2} + x y - 1$ in a factored form.

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Step 1.3.5.1

Rewrite $x^{2} y^{2}$ as ${(x y)}^{2}$ .

$\frac{12 {(x y)}^{2} + x y - 1}{2 y^{2}} = 6$

Step 1.3.5.2

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

$\frac{12 u^{2} + u - 1}{2 y^{2}} = 6$

Step 1.3.5.3

Factor by grouping.

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Step 1.3.5.3.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 12 \cdot - 1 = - 12$ and whose sum is $b = 1$ .

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Step 1.3.5.3.1.1

Multiply by $1$ .

$\frac{12 u^{2} + 1 u - 1}{2 y^{2}} = 6$

Step 1.3.5.3.1.2

Rewrite $1$ as $- 3$ plus $4$

$\frac{12 u^{2} + (- 3 + 4) u - 1}{2 y^{2}} = 6$

Step 1.3.5.3.1.3

Apply the distributive property.

$\frac{12 u^{2} - 3 u + 4 u - 1}{2 y^{2}} = 6$

Step 1.3.5.3.2

Factor out the greatest common factor from each group.

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Step 1.3.5.3.2.1

Group the first two terms and the last two terms.

$\frac{(12 u^{2} - 3 u) + 4 u - 1}{2 y^{2}} = 6$

Step 1.3.5.3.2.2

Factor out the greatest common factor (GCF) from each group.

$\frac{3 u (4 u - 1) + 1 (4 u - 1)}{2 y^{2}} = 6$

Step 1.3.5.3.3

Factor the polynomial by factoring out the greatest common factor, $4 u - 1$ .

$\frac{(4 u - 1) (3 u + 1)}{2 y^{2}} = 6$

Step 1.3.5.4

Replace all occurrences of $u$ with $x y$ .

$\frac{(4 (x y) - 1) (3 (x y) + 1)}{2 y^{2}} = 6$

Step 1.3.5.5

Remove parentheses.

$\frac{(4 x y - 1) (3 x y + 1)}{2 y^{2}} = 6$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 y^{2}, 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 y^{2}$

Step 3

Multiply each term in $\frac{(4 x y - 1) (3 x y + 1)}{2 y^{2}} = 6$ by $2 y^{2}$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{(4 x y - 1) (3 x y + 1)}{2 y^{2}} = 6$ by $2 y^{2}$ .

$\frac{(4 x y - 1) (3 x y + 1)}{2 y^{2}} (2 y^{2}) = 6 (2 y^{2})$

Step 3.2

Simplify the left side.

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Step 3.2.1

Reduce the expression by cancelling the common factors.

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Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$2 \frac{(4 x y - 1) (3 x y + 1)}{2 y^{2}} y^{2} = 6 (2 y^{2})$

Step 3.2.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.2.1

Factor $2$ out of $2 y^{2}$ .

$2 \frac{(4 x y - 1) (3 x y + 1)}{2 (y^{2})} y^{2} = 6 (2 y^{2})$

Step 3.2.1.2.2

Cancel the common factor.

$2 \frac{(4 x y - 1) (3 x y + 1)}{2 y^{2}} y^{2} = 6 (2 y^{2})$

Step 3.2.1.2.3

Rewrite the expression.

$\frac{(4 x y - 1) (3 x y + 1)}{y^{2}} y^{2} = 6 (2 y^{2})$

Step 3.2.1.3

Cancel the common factor of $y^{2}$ .

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Step 3.2.1.3.1

Cancel the common factor.

$\frac{(4 x y - 1) (3 x y + 1)}{y^{2}} y^{2} = 6 (2 y^{2})$

Step 3.2.1.3.2

Rewrite the expression.

$(4 x y - 1) (3 x y + 1) = 6 (2 y^{2})$

Step 3.2.2

Expand $(4 x y - 1) (3 x y + 1)$ using the FOIL Method.

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Step 3.2.2.1

Apply the distributive property.

$4 x y (3 x y + 1) - 1 (3 x y + 1) = 6 (2 y^{2})$

Step 3.2.2.2

Apply the distributive property.

$4 x y (3 x y) + 4 x y \cdot 1 - 1 (3 x y + 1) = 6 (2 y^{2})$

Step 3.2.2.3

Apply the distributive property.

$4 x y (3 x y) + 4 x y \cdot 1 - 1 (3 x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3

Simplify and combine like terms.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 3.2.3.1.1.1

Move $x$ .

$4 (x \cdot x) y (3 y) + 4 x y \cdot 1 - 1 (3 x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3.1.1.2

Multiply $x$ by $x$ .

$4 x^{2} y (3 y) + 4 x y \cdot 1 - 1 (3 x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 3.2.3.1.2.1

Move $y$ .

$4 x^{2} (y \cdot y) \cdot 3 + 4 x y \cdot 1 - 1 (3 x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3.1.2.2

Multiply $y$ by $y$ .

$4 x^{2} y^{2} \cdot 3 + 4 x y \cdot 1 - 1 (3 x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3.1.3

Multiply $3$ by $4$ .

$12 x^{2} y^{2} + 4 x y \cdot 1 - 1 (3 x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3.1.4

Multiply $4$ by $1$ .

$12 x^{2} y^{2} + 4 x y - 1 (3 x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3.1.5

Multiply $3$ by $- 1$ .

$12 x^{2} y^{2} + 4 x y - 3 (x y) - 1 \cdot 1 = 6 (2 y^{2})$

Step 3.2.3.1.6

Multiply $- 1$ by $1$ .

$12 x^{2} y^{2} + 4 x y - 3 x y - 1 = 6 (2 y^{2})$

Step 3.2.3.2

Subtract $3 x y$ from $4 x y$ .

$12 x^{2} y^{2} + 1 x y - 1 = 6 (2 y^{2})$

Step 3.2.4

Multiply $x$ by $1$ .

$12 x^{2} y^{2} + x y - 1 = 6 (2 y^{2})$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $2$ by $6$ .

$12 x^{2} y^{2} + x y - 1 = 12 y^{2}$

Step 4

Solve the equation.

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Step 4.1

Subtract $12 y^{2}$ from both sides of the equation.

$12 x^{2} y^{2} + x y - 1 - 12 y^{2} = 0$

Step 4.2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4.3

Substitute the values $a = 12 x^{2} - 12$ , $b = x$ , and $c = - 1$ into the quadratic formula and solve for $y$ .

$\frac{- x \pm \sqrt{x^{2} - 4 \cdot ((12 x^{2} - 12) \cdot - 1)}}{2 (12 x^{2} - 12)}$

Step 4.4

Simplify.

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Step 4.4.1

Simplify the numerator.

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Step 4.4.1.1

Apply the distributive property.

$y = \frac{- x \pm \sqrt{x^{2} + (- 4 (12 x^{2}) - 4 \cdot - 12) \cdot - 1}}{2 (12 x^{2} - 12)}$

Step 4.4.1.2

Multiply $12$ by $- 4$ .

$y = \frac{- x \pm \sqrt{x^{2} + (- 48 x^{2} - 4 \cdot - 12) \cdot - 1}}{2 (12 x^{2} - 12)}$

Step 4.4.1.3

Multiply $- 4$ by $- 12$ .

$y = \frac{- x \pm \sqrt{x^{2} + (- 48 x^{2} + 48) \cdot - 1}}{2 (12 x^{2} - 12)}$

Step 4.4.1.4

Apply the distributive property.

$y = \frac{- x \pm \sqrt{x^{2} - 48 x^{2} \cdot - 1 + 48 \cdot - 1}}{2 (12 x^{2} - 12)}$

Step 4.4.1.5

Multiply $- 1$ by $- 48$ .

$y = \frac{- x \pm \sqrt{x^{2} + 48 x^{2} + 48 \cdot - 1}}{2 (12 x^{2} - 12)}$

Step 4.4.1.6

Multiply $48$ by $- 1$ .

$y = \frac{- x \pm \sqrt{x^{2} + 48 x^{2} - 48}}{2 (12 x^{2} - 12)}$

Step 4.4.1.7

Add $x^{2}$ and $48 x^{2}$ .

$y = \frac{- x \pm \sqrt{49 x^{2} - 48}}{2 (12 x^{2} - 12)}$

Step 4.4.2

Simplify the denominator.

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Step 4.4.2.1

Factor $12$ out of $12 x^{2} - 12$ .

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Step 4.4.2.1.1

Factor $12$ out of $12 x^{2}$ .

$y = \frac{- x \pm \sqrt{49 x^{2} - 48}}{2 (12 (x^{2}) - 12)}$

Step 4.4.2.1.2

Factor $12$ out of $- 12$ .

$y = \frac{- x \pm \sqrt{49 x^{2} - 48}}{2 (12 (x^{2}) + 12 (- 1))}$

Step 4.4.2.1.3

Factor $12$ out of $12 (x^{2}) + 12 (- 1)$ .

$y = \frac{- x \pm \sqrt{49 x^{2} - 48}}{2 (12 (x^{2} - 1))}$

Step 4.4.2.2

Rewrite $1$ as $1^{2}$ .

$y = \frac{- x \pm \sqrt{49 x^{2} - 48}}{2 (12 (x^{2} - 1^{2}))}$

Step 4.4.2.3

Factor.

$y = \frac{- x \pm \sqrt{49 x^{2} - 48}}{2 \cdot (12 (x + 1) (x - 1))}$

Step 4.4.2.4

Multiply $2$ by $12$ .

$y = \frac{- x \pm \sqrt{49 x^{2} - 48}}{24 (x + 1) (x - 1)}$

Step 4.5

The final answer is the combination of both solutions.

$y = - \frac{x - \sqrt{49 x^{2} - 48}}{24 (x + 1) (x - 1)}$

$y = - \frac{x + \sqrt{49 x^{2} - 48}}{24 (x + 1) (x - 1)}$

$y = - \frac{x - \sqrt{49 x^{2} - 48}}{24 (x + 1) (x - 1)}$

$y = - \frac{x + \sqrt{49 x^{2} - 48}}{24 (x + 1) (x - 1)}$