Finite Math Examples

$h (2 z) = \frac{4 x + 7}{x - 6}$

Step 1

Multiply the equation by $x - 6$ .

$(x - 6) (h \cdot (2 z)) = (\frac{4 x + 7}{x - 6}) (x - 6)$

Step 2

Simplify the left side.

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Step 2.1

Simplify $(x - 6) (h \cdot (2 z))$ .

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$(x - 6) (2 h z) = (\frac{4 x + 7}{x - 6}) (x - 6)$

Step 2.1.2

Apply the distributive property.

$x (2 h z) - 6 (2 h z) = (\frac{4 x + 7}{x - 6}) (x - 6)$

Step 2.1.3

Simplify the expression.

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Step 2.1.3.1

Rewrite using the commutative property of multiplication.

$2 x h z - 6 (2 h z) = (\frac{4 x + 7}{x - 6}) (x - 6)$

Step 2.1.3.2

Multiply $2$ by $- 6$ .

$2 x h z - 12 h z = (\frac{4 x + 7}{x - 6}) (x - 6)$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $x - 6$ .

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Step 3.1.1

Cancel the common factor.

$2 x h z - 12 h z = \frac{4 x + 7}{x - 6} (x - 6)$

Step 3.1.2

Rewrite the expression.

$2 x h z - 12 h z = 4 x + 7$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $4 x$ from both sides of the equation.

$2 x h z - 12 h z - 4 x = 7$

Step 4.2

Add $12 h z$ to both sides of the equation.

$2 x h z - 4 x = 7 + 12 h z$

Step 4.3

Factor $2 x$ out of $2 x h z - 4 x$ .

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Step 4.3.1

Factor $2 x$ out of $2 x h z$ .

$2 x (h z) - 4 x = 7 + 12 h z$

Step 4.3.2

Factor $2 x$ out of $- 4 x$ .

$2 x (h z) + 2 x (- 2) = 7 + 12 h z$

Step 4.3.3

Factor $2 x$ out of $2 x (h z) + 2 x (- 2)$ .

$2 x (h z - 2) = 7 + 12 h z$

Step 4.4

Divide each term in $2 x (h z - 2) = 7 + 12 h z$ by $2 (h z - 2)$ and simplify.

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Step 4.4.1

Divide each term in $2 x (h z - 2) = 7 + 12 h z$ by $2 (h z - 2)$ .

$\frac{2 x (h z - 2)}{2 (h z - 2)} = \frac{7}{2 (h z - 2)} + \frac{12 h z}{2 (h z - 2)}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $2$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{2 x (h z - 2)}{2 (h z - 2)} = \frac{7}{2 (h z - 2)} + \frac{12 h z}{2 (h z - 2)}$

Step 4.4.2.1.2

Rewrite the expression.

$\frac{x (h z - 2)}{h z - 2} = \frac{7}{2 (h z - 2)} + \frac{12 h z}{2 (h z - 2)}$

Step 4.4.2.2

Cancel the common factor of $h z - 2$ .

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Step 4.4.2.2.1

Cancel the common factor.

$\frac{x (h z - 2)}{h z - 2} = \frac{7}{2 (h z - 2)} + \frac{12 h z}{2 (h z - 2)}$

Step 4.4.2.2.2

Divide $x$ by $1$ .

$x = \frac{7}{2 (h z - 2)} + \frac{12 h z}{2 (h z - 2)}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Cancel the common factor of $12$ and $2$ .

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Step 4.4.3.1.1

Factor $2$ out of $12 h z$ .

$x = \frac{7}{2 (h z - 2)} + \frac{2 (6 h z)}{2 (h z - 2)}$

Step 4.4.3.1.2

Cancel the common factors.

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Step 4.4.3.1.2.1

Cancel the common factor.

$x = \frac{7}{2 (h z - 2)} + \frac{2 (6 h z)}{2 (h z - 2)}$

Step 4.4.3.1.2.2

Rewrite the expression.

$x = \frac{7}{2 (h z - 2)} + \frac{6 h z}{h z - 2}$

Step 4.4.3.2

To write $\frac{6 h z}{h z - 2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{7}{2 (h z - 2)} + \frac{6 h z}{h z - 2} \cdot \frac{2}{2}$

Step 4.4.3.3

Write each expression with a common denominator of $2 (h z - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.3.3.1

Multiply $\frac{6 h z}{h z - 2}$ by $\frac{2}{2}$ .

$x = \frac{7}{2 (h z - 2)} + \frac{6 h z \cdot 2}{(h z - 2) \cdot 2}$

Step 4.4.3.3.2

Reorder the factors of $(h z - 2) \cdot 2$ .

$x = \frac{7}{2 (h z - 2)} + \frac{6 h z \cdot 2}{2 (h z - 2)}$

Step 4.4.3.4

Combine the numerators over the common denominator.

$x = \frac{7 + 6 h z \cdot 2}{2 (h z - 2)}$

Step 4.4.3.5

Multiply $2$ by $6$ .

$x = \frac{7 + 12 h z}{2 (h z - 2)}$