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

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

Step 1

Factor $y^{2} + 4 y - 21$ 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.

$\frac{(y - 3) (y + 7)}{y^{2} + 2 y - 35}$

Step 2

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 $2$ .

$- 5, 7$

Write the factored form using these integers.

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

Step 3

Cancel the common factor of $y + 7$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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