Basic Math Examples

$\frac{\frac{y^{2} + 7 y + 6}{y - 5}}{\frac{y^{2} - 8 y - 9}{y - 5}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{y^{2} + 7 y + 6}{y - 5} \cdot \frac{y - 5}{y^{2} - 8 y - 9}$

Step 2

Cancel the common factor of $y - 5$ .

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Step 2.1

Cancel the common factor.

$\frac{y^{2} + 7 y + 6}{y - 5} \cdot \frac{y - 5}{y^{2} - 8 y - 9}$

Step 2.2

Rewrite the expression.

$(y^{2} + 7 y + 6) \frac{1}{y^{2} - 8 y - 9}$

Step 3

Factor $y^{2} - 8 y - 9$ using the AC method.

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Step 3.1

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 $- 9$ and whose sum is $- 8$ .

$- 9, 1$

Step 3.2

Write the factored form using these integers.

$(y^{2} + 7 y + 6) \frac{1}{(y - 9) (y + 1)}$

Step 4

Multiply $y^{2} + 7 y + 6$ by $\frac{1}{(y - 9) (y + 1)}$ .

$\frac{y^{2} + 7 y + 6}{(y - 9) (y + 1)}$

Step 5

Factor $y^{2} + 7 y + 6$ using the AC method.

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Step 5.1

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 $6$ and whose sum is $7$ .

$1, 6$

Step 5.2

Write the factored form using these integers.

$\frac{(y + 1) (y + 6)}{(y - 9) (y + 1)}$

Step 6

Cancel the common factor of $y + 1$ .

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Step 6.1

Cancel the common factor.

$\frac{(y + 1) (y + 6)}{(y - 9) (y + 1)}$

Step 6.2

Rewrite the expression.

$\frac{y + 6}{y - 9}$