Simplify (x^2-81)/(4x^3-36x^2)

$\frac{x^{2} - 81}{4 x^{3} - 36 x^{2}}$

Step 1

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

$\frac{x^{2} - 9^{2}}{4 x^{3} - 36 x^{2}}$

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 $b = 9$ .

$\frac{(x + 9) (x - 9)}{4 x^{3} - 36 x^{2}}$

Step 2

Simplify terms.

Factor $4 x^{2}$ out of $4 x^{3} - 36 x^{2}$ .

Factor $4 x^{2}$ out of $4 x^{3}$ .

$\frac{(x + 9) (x - 9)}{4 x^{2} (x) - 36 x^{2}}$

Factor $4 x^{2}$ out of $- 36 x^{2}$ .

$\frac{(x + 9) (x - 9)}{4 x^{2} (x) + 4 x^{2} (- 9)}$

Factor $4 x^{2}$ out of $4 x^{2} (x) + 4 x^{2} (- 9)$ .

$\frac{(x + 9) (x - 9)}{4 x^{2} (x - 9)}$

Cancel the common factor of $x - 9$ .

Cancel the common factor.

$\frac{(x + 9) (x - 9)}{4 x^{2} (x - 9)}$

Rewrite the expression.

$\frac{x + 9}{4 x^{2}}$