Simplify (x^2-3x-28)/(x^2-2x-35)

$\frac{x^{2} - 3 x - 28}{x^{2} - 2 x - 35}$

Step 1

Factor $x^{2} - 3 x - 28$ 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 $- 28$ and whose sum is $- 3$ .

$- 7, 4$

Write the factored form using these integers.

$\frac{(x - 7) (x + 4)}{x^{2} - 2 x - 35}$

Step 2

Factor $x^{2} - 2 x - 35$ 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 $- 2$ .

$- 7, 5$

Write the factored form using these integers.

$\frac{(x - 7) (x + 4)}{(x - 7) (x + 5)}$

Step 3

Cancel the common factor of $x - 7$ .

Cancel the common factor.

$\frac{(x - 7) (x + 4)}{(x - 7) (x + 5)}$

Rewrite the expression.

$\frac{x + 4}{x + 5}$

Simplify (x^2-3x-28)/(x^2-2x-35)

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