Algebra Examples

$\frac{4}{x - 3} + \frac{9}{x - 6}$

To write $\frac{4}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x - 6}{x - 6}$ .

$\frac{4}{x - 3} \cdot \frac{x - 6}{x - 6} + \frac{9}{x - 6}$

To write $\frac{9}{x - 6}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$\frac{4}{x - 3} \cdot \frac{x - 6}{x - 6} + \frac{9}{x - 6} \cdot \frac{x - 3}{x - 3}$

Write each expression with a common denominator of $(x - 3) (x - 6)$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{4}{x - 3}$ and $\frac{x - 6}{x - 6}$ .

$\frac{4 (x - 6)}{(x - 3) (x - 6)} + \frac{9}{x - 6} \cdot \frac{x - 3}{x - 3}$

Multiply $\frac{9}{x - 6}$ and $\frac{x - 3}{x - 3}$ .

$\frac{4 (x - 6)}{(x - 3) (x - 6)} + \frac{9 (x - 3)}{(x - 6) (x - 3)}$

Reorder the factors of $(x - 6) (x - 3)$ .

$\frac{4 (x - 6)}{(x - 3) (x - 6)} + \frac{9 (x - 3)}{(x - 3) (x - 6)}$

Combine the numerators over the common denominator.

$\frac{4 (x - 6) + 9 (x - 3)}{(x - 3) (x - 6)}$

Simplify the numerator.

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Apply the distributive property.

$\frac{4 x + 4 \cdot - 6 + 9 (x - 3)}{(x - 3) (x - 6)}$

Multiply $4$ by $- 6$ .

$\frac{4 x - 24 + 9 (x - 3)}{(x - 3) (x - 6)}$

Apply the distributive property.

$\frac{4 x - 24 + 9 x + 9 \cdot - 3}{(x - 3) (x - 6)}$

Multiply $9$ by $- 3$ .

$\frac{4 x - 24 + 9 x - 27}{(x - 3) (x - 6)}$

Add $4 x$ and $9 x$ .

$\frac{13 x - 24 - 27}{(x - 3) (x - 6)}$

Subtract $27$ from $- 24$ .

$\frac{13 x - 51}{(x - 3) (x - 6)}$

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