Basic Math Examples

$\frac{3}{x - 6} + \frac{4}{x + 5}$

Step 1

To write

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

$\frac{x + 5}{x + 5}$ .

$\frac{3}{x - 6} \cdot \frac{x + 5}{x + 5} + \frac{4}{x + 5}$

Step 2

To write

$\frac{4}{x + 5}$ as a fraction with a common denominator, multiply by

$\frac{x - 6}{x - 6}$ .

$\frac{3}{x - 6} \cdot \frac{x + 5}{x + 5} + \frac{4}{x + 5} \cdot \frac{x - 6}{x - 6}$

Step 3

Write each expression with a common denominator of

$(x - 6) (x + 5)$ , by multiplying each by an appropriate factor of

$1$ .

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Step 3.1

Multiply

$\frac{3}{x - 6}$ by

$\frac{x + 5}{x + 5}$ .

$\frac{3 (x + 5)}{(x - 6) (x + 5)} + \frac{4}{x + 5} \cdot \frac{x - 6}{x - 6}$

Step 3.2

Multiply

$\frac{4}{x + 5}$ by

$\frac{x - 6}{x - 6}$ .

$\frac{3 (x + 5)}{(x - 6) (x + 5)} + \frac{4 (x - 6)}{(x + 5) (x - 6)}$

Step 3.3

Reorder the factors of

$(x - 6) (x + 5)$ .

$\frac{3 (x + 5)}{(x + 5) (x - 6)} + \frac{4 (x - 6)}{(x + 5) (x - 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (x + 5) + 4 (x - 6)}{(x + 5) (x - 6)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{3 x + 3 \cdot 5 + 4 (x - 6)}{(x + 5) (x - 6)}$

Step 5.2

Multiply

$3$ by

$5$ .

$\frac{3 x + 15 + 4 (x - 6)}{(x + 5) (x - 6)}$

Step 5.3

Apply the distributive property.

$\frac{3 x + 15 + 4 x + 4 \cdot - 6}{(x + 5) (x - 6)}$

Step 5.4

Multiply

$4$ by

$- 6$ .

$\frac{3 x + 15 + 4 x - 24}{(x + 5) (x - 6)}$

Step 5.5

Add

$3 x$ and

$4 x$ .

$\frac{7 x + 15 - 24}{(x + 5) (x - 6)}$

Step 5.6

Subtract

$24$ from

$15$ .

$\frac{7 x - 9}{(x + 5) (x - 6)}$