Algebra Examples

$\frac{5 y + 5}{2} \div \frac{25 y - 20}{40 y^{2} - 32 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 y + 5}{2} \cdot \frac{40 y^{2} - 32 y}{25 y - 20}$

Step 2

Factor $5$ out of $5 y + 5$ .

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Step 2.1

Factor $5$ out of $5 y$ .

$\frac{5 (y) + 5}{2} \cdot \frac{40 y^{2} - 32 y}{25 y - 20}$

Step 2.2

Factor $5$ out of $5$ .

$\frac{5 (y) + 5 (1)}{2} \cdot \frac{40 y^{2} - 32 y}{25 y - 20}$

Step 2.3

Factor $5$ out of $5 (y) + 5 (1)$ .

$\frac{5 (y + 1)}{2} \cdot \frac{40 y^{2} - 32 y}{25 y - 20}$

Step 3

Factor $8 y$ out of $40 y^{2} - 32 y$ .

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Step 3.1

Factor $8 y$ out of $40 y^{2}$ .

$\frac{5 (y + 1)}{2} \cdot \frac{8 y (5 y) - 32 y}{25 y - 20}$

Step 3.2

Factor $8 y$ out of $- 32 y$ .

$\frac{5 (y + 1)}{2} \cdot \frac{8 y (5 y) + 8 y (- 4)}{25 y - 20}$

Step 3.3

Factor $8 y$ out of $8 y (5 y) + 8 y (- 4)$ .

$\frac{5 (y + 1)}{2} \cdot \frac{8 y (5 y - 4)}{25 y - 20}$

Step 4

Factor $5$ out of $25 y - 20$ .

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Step 4.1

Factor $5$ out of $25 y$ .

$\frac{5 (y + 1)}{2} \cdot \frac{8 y (5 y - 4)}{5 (5 y) - 20}$

Step 4.2

Factor $5$ out of $- 20$ .

$\frac{5 (y + 1)}{2} \cdot \frac{8 y (5 y - 4)}{5 (5 y) + 5 (- 4)}$

Step 4.3

Factor $5$ out of $5 (5 y) + 5 (- 4)$ .

$\frac{5 (y + 1)}{2} \cdot \frac{8 y (5 y - 4)}{5 (5 y - 4)}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$\frac{5 (y + 1)}{2} \cdot \frac{8 y (5 y - 4)}{5 (5 y - 4)}$

Step 5.2

Rewrite the expression.

$\frac{y + 1}{2} \cdot \frac{8 y (5 y - 4)}{5 y - 4}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $8 y (5 y - 4)$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $5 y - 4$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Divide $4 y$ by $1$ .

$(y + 1) (4 y)$

Step 8

Apply the distributive property.

$y (4 y) + 1 (4 y)$

Step 9

Simplify the expression.

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Step 9.1

Rewrite using the commutative property of multiplication.

$4 y \cdot y + 1 (4 y)$

Step 9.2

Multiply $4 y$ by $1$ .

$4 y \cdot y + 4 y$

Step 10

Multiply $y$ by $y$ by adding the exponents.

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Step 10.1

Move $y$ .

$4 (y \cdot y) + 4 y$

Step 10.2

Multiply $y$ by $y$ .

$4 y^{2} + 4 y$