Basic Math Examples

$\frac{2}{x - 6} + \frac{3}{x + 5}$

Step 1

To write $\frac{2}{x - 6}$ as a fraction with a common denominator, multiply by $\frac{x + 5}{x + 5}$ .

$\frac{2}{x - 6} \cdot \frac{x + 5}{x + 5} + \frac{3}{x + 5}$

Step 2

To write $\frac{3}{x + 5}$ as a fraction with a common denominator, multiply by $\frac{x - 6}{x - 6}$ .

$\frac{2}{x - 6} \cdot \frac{x + 5}{x + 5} + \frac{3}{x + 5} \cdot \frac{x - 6}{x - 6}$

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 $\frac{2}{x - 6}$ by $\frac{x + 5}{x + 5}$ .

$\frac{2 (x + 5)}{(x - 6) (x + 5)} + \frac{3}{x + 5} \cdot \frac{x - 6}{x - 6}$

Step 3.2

Multiply $\frac{3}{x + 5}$ by $\frac{x - 6}{x - 6}$ .

$\frac{2 (x + 5)}{(x - 6) (x + 5)} + \frac{3 (x - 6)}{(x + 5) (x - 6)}$

Step 3.3

Reorder the factors of $(x - 6) (x + 5)$ .

$\frac{2 (x + 5)}{(x + 5) (x - 6)} + \frac{3 (x - 6)}{(x + 5) (x - 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 (x + 5) + 3 (x - 6)}{(x + 5) (x - 6)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{2 x + 2 \cdot 5 + 3 (x - 6)}{(x + 5) (x - 6)}$

Step 5.2

Multiply $2$ by $5$ .

$\frac{2 x + 10 + 3 (x - 6)}{(x + 5) (x - 6)}$

Step 5.3

Apply the distributive property.

$\frac{2 x + 10 + 3 x + 3 \cdot - 6}{(x + 5) (x - 6)}$

Step 5.4

Multiply $3$ by $- 6$ .

$\frac{2 x + 10 + 3 x - 18}{(x + 5) (x - 6)}$

Step 5.5

Add $2 x$ and $3 x$ .

$\frac{5 x + 10 - 18}{(x + 5) (x - 6)}$

Step 5.6

Subtract $18$ from $10$ .

$\frac{5 x - 8}{(x + 5) (x - 6)}$