Simplify (x^2+2x-35)/(x^2+4x-21)

$\frac{x^{2} + 2 x - 35}{x^{2} + 4 x - 21}$

Step 1

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 $2$ .

$- 5, 7$

Write the factored form using these integers.

$\frac{(x - 5) (x + 7)}{x^{2} + 4 x - 21}$

Step 2

Factor $x^{2} + 4 x - 21$ 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 $- 21$ and whose sum is $4$ .

$- 3, 7$

Write the factored form using these integers.

$\frac{(x - 5) (x + 7)}{(x - 3) (x + 7)}$

Step 3

Cancel the common factor of $x + 7$ .

Cancel the common factor.

$\frac{(x - 5) (x + 7)}{(x - 3) (x + 7)}$

Rewrite the expression.

$\frac{x - 5}{x - 3}$

Simplify (x^2+2x-35)/(x^2+4x-21)

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