Algebra Examples

$\frac{y^{2} + 2 y - 35}{y^{2} - 5 y - 3 y + 15}$

Step 1

Factor $y^{2} + 2 y - 35$ using the AC method.

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Step 1.1

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 $2$ .

$- 5, 7$

Step 1.2

Write the factored form using these integers.

$\frac{(y - 5) (y + 7)}{y^{2} - 5 y - 3 y + 15}$

Step 2

Simplify the denominator.

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Step 2.1

Reorder terms.

$\frac{(y - 5) (y + 7)}{y^{2} - 3 y - 5 y + 15}$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$\frac{(y - 5) (y + 7)}{(y^{2} - 3 y) - 5 y + 15}$

Step 2.2.2

Factor out the greatest common factor (GCF) from each group.

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

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $y - 3$ .

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

Step 3

Cancel the common factor of $y - 5$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{y + 7}{y - 3}$