Algebra Examples

$\frac{3}{x + 1} + \frac{6}{x - 3}$

To write $\frac{3}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$\frac{3}{x + 1} \frac{x - 3}{x - 3} + \frac{6}{x - 3}$

To write $\frac{6}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{3}{x + 1} \frac{x - 3}{x - 3} + \frac{6}{x - 3} \frac{x + 1}{x + 1}$

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

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Combine.

$\frac{3 (x - 3)}{(x + 1) (x - 3)} + \frac{6}{x - 3} \frac{x + 1}{x + 1}$

Combine.

$\frac{3 (x - 3)}{(x + 1) (x - 3)} + \frac{6 (x + 1)}{(x - 3) (x + 1)}$

Reorder terms.

$\frac{3 (x - 3)}{(x + 1) (x - 3)} + \frac{6 (x + 1)}{(x + 1) (x - 3)}$

Combine the numerators over the common denominator.

$\frac{3 (x - 3) + 6 (x + 1)}{(x + 1) (x - 3)}$

Simplify the numerator.

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Factor $3$ out of $3 (x - 3) + 6 (x + 1)$ .

$\frac{3 (x - 3 + 2 (x + 1))}{(x + 1) (x - 3)}$

Apply the distributive property.

$\frac{3 (x - 3 + (2 x + 2 \cdot 1))}{(x + 1) (x - 3)}$

Multiply $2$ by $1$ to get $2$ .

$\frac{3 (x - 3 + (2 x + 2))}{(x + 1) (x - 3)}$

Remove parentheses.

$\frac{3 (x - 3 + 2 x + 2)}{(x + 1) (x - 3)}$

Add $x$ and $2 x$ to get $3 x$ .

$\frac{3 (3 x - 3 + 2)}{(x + 1) (x - 3)}$

Add $- 3$ and $2$ to get $- 1$ .

$\frac{3 (3 x - 1)}{(x + 1) (x - 3)}$

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