Trigonometry Examples

$\frac{6 b}{b - 4} - \frac{1}{b + 1}$

Step 1

To write $\frac{6 b}{b - 4}$ as a fraction with a common denominator, multiply by $\frac{b + 1}{b + 1}$ .

$\frac{6 b}{b - 4} \cdot \frac{b + 1}{b + 1} - \frac{1}{b + 1}$

Step 2

To write $- \frac{1}{b + 1}$ as a fraction with a common denominator, multiply by $\frac{b - 4}{b - 4}$ .

$\frac{6 b}{b - 4} \cdot \frac{b + 1}{b + 1} - \frac{1}{b + 1} \cdot \frac{b - 4}{b - 4}$

Step 3

Write each expression with a common denominator of $(b - 4) (b + 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6 b}{b - 4}$ by $\frac{b + 1}{b + 1}$ .

$\frac{6 b (b + 1)}{(b - 4) (b + 1)} - \frac{1}{b + 1} \cdot \frac{b - 4}{b - 4}$

Step 3.2

Multiply $\frac{1}{b + 1}$ by $\frac{b - 4}{b - 4}$ .

$\frac{6 b (b + 1)}{(b - 4) (b + 1)} - \frac{b - 4}{(b + 1) (b - 4)}$

Step 3.3

Reorder the factors of $(b - 4) (b + 1)$ .

$\frac{6 b (b + 1)}{(b + 1) (b - 4)} - \frac{b - 4}{(b + 1) (b - 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 b (b + 1) - (b - 4)}{(b + 1) (b - 4)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{6 b \cdot b + 6 b \cdot 1 - (b - 4)}{(b + 1) (b - 4)}$

Step 5.2

Multiply $b$ by $b$ by adding the exponents.

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Step 5.2.1

Move $b$ .

$\frac{6 (b \cdot b) + 6 b \cdot 1 - (b - 4)}{(b + 1) (b - 4)}$

Step 5.2.2

Multiply $b$ by $b$ .

$\frac{6 b^{2} + 6 b \cdot 1 - (b - 4)}{(b + 1) (b - 4)}$

Step 5.3

Multiply $6$ by $1$ .

$\frac{6 b^{2} + 6 b - (b - 4)}{(b + 1) (b - 4)}$

Step 5.4

Apply the distributive property.

$\frac{6 b^{2} + 6 b - b - - 4}{(b + 1) (b - 4)}$

Step 5.5

Multiply $- 1$ by $- 4$ .

$\frac{6 b^{2} + 6 b - b + 4}{(b + 1) (b - 4)}$

Step 5.6

Subtract $b$ from $6 b$ .

$\frac{6 b^{2} + 5 b + 4}{(b + 1) (b - 4)}$