Solve for x 2=(6x^2-2x+5)/(3x^2-2)

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

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.

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

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

Remove parentheses.

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

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.

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

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

Simplify the left side.

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Apply the distributive property.

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

Multiply.

Multiply $3$ by $2$ .

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

Multiply $2$ by $- 2$ .

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

Step 4

Solve the equation.

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

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

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

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

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

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

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

$- 2 x + 5 = - 4$

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

Subtract $5$ from both sides of the equation.

$- 2 x = - 4 - 5$

Subtract $5$ from $- 4$ .

$- 2 x = - 9$

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

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

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

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:

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

Solve for x 2=(6x^2-2x+5)/(3x^2-2)

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