Solve for x (x^2)/(2x-6)=9/(6x-18)

$\frac{x^{2}}{2 x - 6} = \frac{9}{6 x - 18}$

Factor each term.

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Factor $2$ out of $2 x - 6$ .

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Factor $2$ out of $2 x$ .

$\frac{x^{2}}{2 (x) - 6} = \frac{9}{6 x - 18}$

Factor $2$ out of $- 6$ .

$\frac{x^{2}}{2 x + 2 \cdot - 3} = \frac{9}{6 x - 18}$

Factor $2$ out of $2 x + 2 \cdot - 3$ .

$\frac{x^{2}}{2 (x - 3)} = \frac{9}{6 x - 18}$

Factor $6$ out of $6 x - 18$ .

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Factor $6$ out of $6 x$ .

$\frac{x^{2}}{2 (x - 3)} = \frac{9}{6 (x) - 18}$

Factor $6$ out of $- 18$ .

$\frac{x^{2}}{2 (x - 3)} = \frac{9}{6 x + 6 \cdot - 3}$

Factor $6$ out of $6 x + 6 \cdot - 3$ .

$\frac{x^{2}}{2 (x - 3)} = \frac{9}{6 (x - 3)}$

Reduce the expression $\frac{9}{6 (x - 3)}$ by cancelling the common factors.

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Factor $3$ out of $9$ .

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

Factor $3$ out of $6 (x - 3)$ .

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

Cancel the common factor.

$\frac{x^{2}}{2 (x - 3)} = \frac{3 \cdot 3}{3 (2 (x - 3))}$

Rewrite the expression.

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x^{2} = 3$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{3}, - \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{3}, - \sqrt{3}$

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$

Solve for x (x^2)/(2x-6)=9/(6x-18)

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