Basic Math Examples

$\frac{4 y^{2} - 25}{10} \div \frac{18 y - 45}{18}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 y^{2} - 25}{10} \cdot \frac{18}{18 y - 45}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $10$ .

$\frac{4 y^{2} - 25}{2 (5)} \cdot \frac{18}{18 y - 45}$

Step 2.1.2

Factor $2$ out of $18$ .

$\frac{4 y^{2} - 25}{2 \cdot 5} \cdot \frac{2 \cdot 9}{18 y - 45}$

Step 2.1.3

Cancel the common factor.

$\frac{4 y^{2} - 25}{2 \cdot 5} \cdot \frac{2 \cdot 9}{18 y - 45}$

Step 2.1.4

Rewrite the expression.

$\frac{4 y^{2} - 25}{5} \cdot \frac{9}{18 y - 45}$

Step 2.2

Multiply $\frac{4 y^{2} - 25}{5}$ by $\frac{9}{18 y - 45}$ .

$\frac{(4 y^{2} - 25) \cdot 9}{5 (18 y - 45)}$

Step 2.3

Cancel the common factor of $9$ and $18 y - 45$ .

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Step 2.3.1

Factor $9$ out of $(4 y^{2} - 25) \cdot 9$ .

$\frac{9 \cdot (4 y^{2} - 25)}{5 (18 y - 45)}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $9$ out of $5 (18 y - 45)$ .

$\frac{9 \cdot (4 y^{2} - 25)}{9 (5 (2 y - 5))}$

Step 2.3.2.2

Cancel the common factor.

$\frac{9 \cdot (4 y^{2} - 25)}{9 (5 (2 y - 5))}$

Step 2.3.2.3

Rewrite the expression.

$\frac{4 y^{2} - 25}{5 (2 y - 5)}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $4 y^{2}$ as ${(2 y)}^{2}$ .

$\frac{{(2 y)}^{2} - 25}{5 (2 y - 5)}$

Step 3.2

Rewrite $25$ as $5^{2}$ .

$\frac{{(2 y)}^{2} - 5^{2}}{5 (2 y - 5)}$

Step 3.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 y$ and $b = 5$ .

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

Step 4

Cancel the common factor of $2 y - 5$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{2 y + 5}{5}$