Algebra Examples

$2 = \frac{6 x^{2} - 2 x + 5}{3 x^{2} - 2}$

Step 1

Rewrite the equation as $\frac{6 x^{2} - 2 x + 5}{3 x^{2} - 2} = 2$ .

$\frac{6 x^{2} - 2 x + 5}{3 x^{2} - 2} = 2$

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.

$3 x^{2} - 2, 1$

Step 2.2

Remove parentheses.

$3 x^{2} - 2, 1$

Step 2.3

The LCM of one and any expression is the expression.

$3 x^{2} - 2$

Step 3

Multiply each term in $\frac{6 x^{2} - 2 x + 5}{3 x^{2} - 2} = 2$ by $3 x^{2} - 2$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{6 x^{2} - 2 x + 5}{3 x^{2} - 2} = 2$ by $3 x^{2} - 2$ .

$\frac{6 x^{2} - 2 x + 5}{3 x^{2} - 2} (3 x^{2} - 2) = 2 (3 x^{2} - 2)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3 x^{2} - 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 x^{2} - 2 x + 5}{3 x^{2} - 2} (3 x^{2} - 2) = 2 (3 x^{2} - 2)$

Step 3.2.1.2

Rewrite the expression.

$6 x^{2} - 2 x + 5 = 2 (3 x^{2} - 2)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$6 x^{2} - 2 x + 5 = 2 (3 x^{2}) + 2 \cdot - 2$

Step 3.3.2

Multiply.

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Step 3.3.2.1

Multiply $3$ by $2$ .

$6 x^{2} - 2 x + 5 = 6 x^{2} + 2 \cdot - 2$

Step 3.3.2.2

Multiply $2$ by $- 2$ .

$6 x^{2} - 2 x + 5 = 6 x^{2} - 4$

Step 4

Solve the equation.

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Step 4.1

Move all terms containing $x$ to the left side of the equation.

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Step 4.1.1

Subtract $6 x^{2}$ from both sides of the equation.

$6 x^{2} - 2 x + 5 - 6 x^{2} = - 4$

Step 4.1.2

Combine the opposite terms in $6 x^{2} - 2 x + 5 - 6 x^{2}$ .

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Step 4.1.2.1

Subtract $6 x^{2}$ from $6 x^{2}$ .

$- 2 x + 5 + 0 = - 4$

Step 4.1.2.2

Add $- 2 x + 5$ and $0$ .

$- 2 x + 5 = - 4$

Step 4.2

Move all terms not containing $x$ to the right side of the equation.

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Step 4.2.1

Subtract $5$ from both sides of the equation.

$- 2 x = - 4 - 5$

Step 4.2.2

Subtract $5$ from $- 4$ .

$- 2 x = - 9$

Step 4.3

Divide each term in $- 2 x = - 9$ by $- 2$ and simplify.

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Step 4.3.1

Divide each term in $- 2 x = - 9$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 9}{- 2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 9}{- 2}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 9}{- 2}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{9}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{2}$

Decimal Form:

$x = 4.5$

Mixed Number Form:

$x = 4 \frac{1}{2}$