Simplify (y^2-2y-35)/(y^2+14y+45)

$\frac{y^{2} - 2 y - 35}{y^{2} + 14 y + 45}$

Step 1

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

$\frac{(y - 7) (y + 5)}{y^{2} + 14 y + 45}$

Step 2

Factor $y^{2} + 14 y + 45$ 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 $45$ and whose sum is $14$ .

$5, 9$

Write the factored form using these integers.

$\frac{(y - 7) (y + 5)}{(y + 5) (y + 9)}$

Step 3

Cancel the common factor of $y + 5$ .

Cancel the common factor.

$\frac{(y - 7) (y + 5)}{(y + 5) (y + 9)}$

Rewrite the expression.

$\frac{y - 7}{y + 9}$

Simplify (y^2-2y-35)/(y^2+14y+45)

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