Trigonometry Examples

$\frac{y}{y + 3} - \frac{2 y - 6}{y^{2} - 9}$

Step 1

Simplify each term.

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Step 1.1

Factor $2$ out of $2 y - 6$ .

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Step 1.1.1

Factor $2$ out of $2 y$ .

$\frac{y}{y + 3} - \frac{2 (y) - 6}{y^{2} - 9}$

Step 1.1.2

Factor $2$ out of $- 6$ .

$\frac{y}{y + 3} - \frac{2 y + 2 \cdot - 3}{y^{2} - 9}$

Step 1.1.3

Factor $2$ out of $2 y + 2 \cdot - 3$ .

$\frac{y}{y + 3} - \frac{2 (y - 3)}{y^{2} - 9}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Rewrite $9$ as $3^{2}$ .

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

Step 1.2.2

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 $b = 3$ .

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

Step 1.3

Cancel the common factor of $y - 3$ .

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Step 1.3.1

Cancel the common factor.

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

Step 1.3.2

Rewrite the expression.

$\frac{y}{y + 3} - \frac{2}{y + 3}$

Step 2

Combine the numerators over the common denominator.

$\frac{y - 2}{y + 3}$