Basic Math Examples

$\frac{1 - \frac{5}{y}}{y - \frac{25}{y}}$

Step 1

Multiply the numerator and denominator of the fraction by $y$ .

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Step 1.1

Multiply $\frac{1 - \frac{5}{y}}{y - \frac{25}{y}}$ by $\frac{y}{y}$ .

$\frac{y}{y} \cdot \frac{1 - \frac{5}{y}}{y - \frac{25}{y}}$

Step 1.2

Combine.

$\frac{y (1 - \frac{5}{y})}{y (y - \frac{25}{y})}$

Step 2

Apply the distributive property.

$\frac{y \cdot 1 + y (- \frac{5}{y})}{y \cdot y + y (- \frac{25}{y})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $y$ .

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Step 3.1.1

Move the leading negative in $- \frac{5}{y}$ into the numerator.

$\frac{y \cdot 1 + y \frac{- 5}{y}}{y \cdot y + y (- \frac{25}{y})}$

Step 3.1.2

Cancel the common factor.

$\frac{y \cdot 1 + y \frac{- 5}{y}}{y \cdot y + y (- \frac{25}{y})}$

Step 3.1.3

Rewrite the expression.

$\frac{y \cdot 1 - 5}{y \cdot y + y (- \frac{25}{y})}$

Step 3.2

Cancel the common factor of $y$ .

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Step 3.2.1

Move the leading negative in $- \frac{25}{y}$ into the numerator.

$\frac{y \cdot 1 - 5}{y \cdot y + y \frac{- 25}{y}}$

Step 3.2.2

Cancel the common factor.

$\frac{y \cdot 1 - 5}{y \cdot y + y \frac{- 25}{y}}$

Step 3.2.3

Rewrite the expression.

$\frac{y \cdot 1 - 5}{y \cdot y - 25}$

Step 4

Multiply $y$ by $1$ .

$\frac{y - 5}{y \cdot y - 25}$

Step 5

Simplify the denominator.

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Step 5.1

Raise $y$ to the power of $1$ .

$\frac{y - 5}{y^{1} y - 25}$

Step 5.2

Raise $y$ to the power of $1$ .

$\frac{y - 5}{y^{1} y^{1} - 25}$

Step 5.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y - 5}{y^{1 + 1} - 25}$

Step 5.4

Add $1$ and $1$ .

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

Step 5.5

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

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

Step 5.6

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

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

Step 6

Cancel the common factor of $y - 5$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{1}{y + 5}$