Simplify (x^2-25)/(x^2-12x+35)

$\frac{x^{2} - 25}{x^{2} - 12 x + 35}$

Step 1

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{x^{2} - 5^{2}}{x^{2} - 12 x + 35}$

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 $b = 5$ .

$\frac{(x + 5) (x - 5)}{x^{2} - 12 x + 35}$

Step 2

Factor $x^{2} - 12 x + 35$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $35$ and whose sum is $- 12$ .

$- 7, - 5$

Write the factored form using these integers.

$\frac{(x + 5) (x - 5)}{(x - 7) (x - 5)}$

Step 3

Cancel the common factor of $x - 5$ .

Cancel the common factor.

$\frac{(x + 5) (x - 5)}{(x - 7) (x - 5)}$

Rewrite the expression.

$\frac{x + 5}{x - 7}$

Simplify (x^2-25)/(x^2-12x+35)

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