Simplify (3x^2-27)/(18-6x)

$\frac{3 x^{2} - 27}{18 - 6 x}$

Step 1

Cancel the common factor of $3 x^{2} - 27$ and $18 - 6 x$ .

Factor $3$ out of $3 x^{2}$ .

$\frac{3 (x^{2}) - 27}{18 - 6 x}$

Factor $3$ out of $- 27$ .

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

Factor $3$ out of $3 x^{2} + 3 \cdot - 9$ .

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

Cancel the common factors.

Factor $3$ out of $18$ .

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

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

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

Factor $3$ out of $3 (6) + 3 (- 2 x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{x^{2} - 3^{2}}{6 - 2 x}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

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

Step 3

Simplify terms.

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

Factor $2$ out of $6$ .

$\frac{(x + 3) (x - 3)}{2 (3) - 2 x}$

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

$\frac{(x + 3) (x - 3)}{2 (3) + 2 (- x)}$

Factor $2$ out of $2 (3) + 2 (- x)$ .

$\frac{(x + 3) (x - 3)}{2 (3 - x)}$

Cancel the common factor of $x - 3$ and $3 - x$ .

Factor $- 1$ out of $x$ .

$\frac{(x + 3) (- 1 (- x) - 3)}{2 (3 - x)}$

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{(x + 3) (- 1 (- x) - 1 (3))}{2 (3 - x)}$

Factor $- 1$ out of $- 1 (- x) - 1 (3)$ .

$\frac{(x + 3) (- 1 (- x + 3))}{2 (3 - x)}$

Reorder terms.

$\frac{(x + 3) (- 1 (- x + 3))}{2 (- x + 3)}$

Cancel the common factor.

$\frac{(x + 3) (- 1 (- x + 3))}{2 (- x + 3)}$

Rewrite the expression.

$\frac{(x + 3) \cdot (- 1)}{2}$

Simplify the expression.

Move $- 1$ to the left of $x + 3$ .

$\frac{- 1 \cdot (x + 3)}{2}$

Move the negative in front of the fraction.

$- \frac{x + 3}{2}$

Simplify (3x^2-27)/(18-6x)

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