Algebra Examples

$\frac{6}{y - 5} - \frac{y + 5}{y^{2} - 25}$

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

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

$\frac{6}{y - 5} - \frac{y + 5}{y^{2} - 5^{2}}$

Step 1.1.2

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 $b = 5$ .

$\frac{6}{y - 5} - \frac{y + 5}{(y + 5) (y - 5)}$

Step 1.2

Cancel the common factor of $y + 5$ .

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Step 1.2.1

Cancel the common factor.

$\frac{6}{y - 5} - \frac{y + 5}{(y + 5) (y - 5)}$

Step 1.2.2

Rewrite the expression.

$\frac{6}{y - 5} - \frac{1}{y - 5}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{6 - 1}{y - 5}$

Step 2.2

Subtract $1$ from $6$ .

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