Trigonometry Examples

$\frac{b^{2}}{b - 3} + \frac{9}{3 - b}$

Step 1

Simplify terms.

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Step 1.1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{b^{2}}{b - 3} + \frac{9}{- 1 (- 3) - b}$

Step 1.2

Factor $- 1$ out of $- b$ .

$\frac{b^{2}}{b - 3} + \frac{9}{- 1 (- 3) - (b)}$

Step 1.3

Factor $- 1$ out of $- 1 (- 3) - (b)$ .

$\frac{b^{2}}{b - 3} + \frac{9}{- 1 (- 3 + b)}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{9}{- 1 (- 3 + b)}$ to the numerator.

$\frac{b^{2}}{b - 3} + \frac{- 1 \cdot 9}{- 3 + b}$

Step 1.4.2

Reorder terms.

$\frac{b^{2}}{b - 3} + \frac{- 1 \cdot 9}{b - 3}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{b^{2} - 1 \cdot 9}{b - 3}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{b^{2} - 3^{2}}{b - 3}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = b$ and $b = 3$ .

$\frac{(b + 3) (b - 3)}{b - 3}$

Step 3

Cancel the common factor of $b - 3$ .

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Step 3.1

Cancel the common factor.

$\frac{(b + 3) (b - 3)}{b - 3}$

Step 3.2

Divide $b + 3$ by $1$ .

$b + 3$