Basic Math Examples

$\frac{y^{2} - 13 y + 40}{y + 7} \div \frac{y^{2} + 3 y - 40}{y + 7}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{y^{2} - 13 y + 40}{y + 7} \cdot \frac{y + 7}{y^{2} + 3 y - 40}$

Step 2

Cancel the common factor of $y + 7$ .

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Step 2.1

Cancel the common factor.

$\frac{y^{2} - 13 y + 40}{y + 7} \cdot \frac{y + 7}{y^{2} + 3 y - 40}$

Step 2.2

Rewrite the expression.

$(y^{2} - 13 y + 40) \frac{1}{y^{2} + 3 y - 40}$

Step 3

Factor $y^{2} + 3 y - 40$ 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 $- 40$ and whose sum is $3$ .

$- 5, 8$

Step 3.2

Write the factored form using these integers.

$(y^{2} - 13 y + 40) \frac{1}{(y - 5) (y + 8)}$

Step 4

Multiply $y^{2} - 13 y + 40$ by $\frac{1}{(y - 5) (y + 8)}$ .

$\frac{y^{2} - 13 y + 40}{(y - 5) (y + 8)}$

Step 5

Factor $y^{2} - 13 y + 40$ 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 $40$ and whose sum is $- 13$ .

$- 8, - 5$

Step 5.2

Write the factored form using these integers.

$\frac{(y - 8) (y - 5)}{(y - 5) (y + 8)}$

Step 6

Cancel the common factor of $y - 5$ .

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Step 6.1

Cancel the common factor.

$\frac{(y - 8) (y - 5)}{(y - 5) (y + 8)}$

Step 6.2

Rewrite the expression.

$\frac{y - 8}{y + 8}$