Simplify (x^2+7x+10)/(x^2-3x-10)

$\frac{x^{2} + 7 x + 10}{x^{2} - 3 x - 10}$

Step 1

Factor $x^{2} + 7 x + 10$ 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 $10$ and whose sum is $7$ .

$2, 5$

Write the factored form using these integers.

$\frac{(x + 2) (x + 5)}{x^{2} - 3 x - 10}$

Step 2

Factor $x^{2} - 3 x - 10$ 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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify (x^2+7x+10)/(x^2-3x-10)

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