Basic Math Examples

$\frac{- 4 y - 11}{y^{2} + 7 y + 10}$

Step 1

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

$2, 5$

Step 1.2

Write the factored form using these integers.

$\frac{- 4 y - 11}{(y + 2) (y + 5)}$

Step 2

Simplify with factoring out.

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Step 2.1

Factor $- 1$ out of $- 4 y$ .

$\frac{- (4 y) - 11}{(y + 2) (y + 5)}$

Step 2.2

Rewrite $- 11$ as $- 1 (11)$ .

$\frac{- (4 y) - 1 (11)}{(y + 2) (y + 5)}$

Step 2.3

Factor $- 1$ out of $- (4 y) - 1 (11)$ .

$\frac{- (4 y + 11)}{(y + 2) (y + 5)}$

Step 2.4

Simplify the expression.

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Step 2.4.1

Rewrite $- (4 y + 11)$ as $- 1 (4 y + 11)$ .

$\frac{- 1 (4 y + 11)}{(y + 2) (y + 5)}$

Step 2.4.2

Move the negative in front of the fraction.

$- \frac{4 y + 11}{(y + 2) (y + 5)}$