Basic Math Examples

$\frac{7 y + 2}{3 y - 23 y + 30} \cdot \frac{24 y - 40}{7 y + 2}$

Step 1

Simplify the denominator.

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Step 1.1

Subtract $23 y$ from $3 y$ .

$\frac{7 y + 2}{- 20 y + 30} \cdot \frac{24 y - 40}{7 y + 2}$

Step 1.2

Factor $10$ out of $- 20 y + 30$ .

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Step 1.2.1

Factor $10$ out of $- 20 y$ .

$\frac{7 y + 2}{10 (- 2 y) + 30} \cdot \frac{24 y - 40}{7 y + 2}$

Step 1.2.2

Factor $10$ out of $30$ .

$\frac{7 y + 2}{10 (- 2 y) + 10 (3)} \cdot \frac{24 y - 40}{7 y + 2}$

Step 1.2.3

Factor $10$ out of $10 (- 2 y) + 10 (3)$ .

$\frac{7 y + 2}{10 (- 2 y + 3)} \cdot \frac{24 y - 40}{7 y + 2}$

Step 2

Simplify terms.

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Step 2.1

Factor $8$ out of $24 y - 40$ .

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Step 2.1.1

Factor $8$ out of $24 y$ .

$\frac{7 y + 2}{10 (- 2 y + 3)} \cdot \frac{8 (3 y) - 40}{7 y + 2}$

Step 2.1.2

Factor $8$ out of $- 40$ .

$\frac{7 y + 2}{10 (- 2 y + 3)} \cdot \frac{8 (3 y) + 8 (- 5)}{7 y + 2}$

Step 2.1.3

Factor $8$ out of $8 (3 y) + 8 (- 5)$ .

$\frac{7 y + 2}{10 (- 2 y + 3)} \cdot \frac{8 (3 y - 5)}{7 y + 2}$

Step 2.2

Cancel the common factor of $7 y + 2$ .

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Step 2.2.1

Cancel the common factor.

$\frac{7 y + 2}{10 (- 2 y + 3)} \cdot \frac{8 (3 y - 5)}{7 y + 2}$

Step 2.2.2

Rewrite the expression.

$\frac{1}{10 (- 2 y + 3)} \cdot (8 (3 y - 5))$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $10 (- 2 y + 3)$ .

$\frac{1}{2 (5 (- 2 y + 3))} \cdot (8 (3 y - 5))$

Step 2.3.2

Factor $2$ out of $8 (3 y - 5)$ .

$\frac{1}{2 (5 (- 2 y + 3))} \cdot (2 (4 (3 y - 5)))$

Step 2.3.3

Cancel the common factor.

$\frac{1}{2 (5 (- 2 y + 3))} \cdot (2 (4 (3 y - 5)))$

Step 2.3.4

Rewrite the expression.

$\frac{1}{5 (- 2 y + 3)} \cdot (4 (3 y - 5))$

Step 2.4

Combine $4$ and $\frac{1}{5 (- 2 y + 3)}$ .

$\frac{4}{5 (- 2 y + 3)} \cdot (3 y - 5)$

Step 2.5

Multiply $\frac{4}{5 (- 2 y + 3)}$ by $3 y - 5$ .

$\frac{4 (3 y - 5)}{5 (- 2 y + 3)}$

Step 2.6

Factor $- 1$ out of $- 2 y$ .

$\frac{4 (3 y - 5)}{5 (- (2 y) + 3)}$

Step 2.7

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{4 (3 y - 5)}{5 (- (2 y) - 1 (- 3))}$

Step 2.8

Factor $- 1$ out of $- (2 y) - 1 (- 3)$ .

$\frac{4 (3 y - 5)}{5 (- (2 y - 3))}$

Step 2.9

Rewrite negatives.

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Step 2.9.1

Rewrite $- (2 y - 3)$ as $- 1 (2 y - 3)$ .

$\frac{4 (3 y - 5)}{5 (- 1 (2 y - 3))}$

Step 2.9.2

Move the negative in front of the fraction.

$- \frac{4 (3 y - 5)}{5 (2 y - 3)}$