Pre-Algebra Examples

$\frac{6}{x - 4} + \frac{3}{x + 1}$

Step 1

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

$\frac{6}{x - 4} \cdot \frac{x + 1}{x + 1} + \frac{3}{x + 1}$

Step 2

To write $\frac{3}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$\frac{6}{x - 4} \cdot \frac{x + 1}{x + 1} + \frac{3}{x + 1} \cdot \frac{x - 4}{x - 4}$

Step 3

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

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Step 3.1

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

$\frac{6 (x + 1)}{(x - 4) (x + 1)} + \frac{3}{x + 1} \cdot \frac{x - 4}{x - 4}$

Step 3.2

Multiply $\frac{3}{x + 1}$ by $\frac{x - 4}{x - 4}$ .

$\frac{6 (x + 1)}{(x - 4) (x + 1)} + \frac{3 (x - 4)}{(x + 1) (x - 4)}$

Step 3.3

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

$\frac{6 (x + 1)}{(x + 1) (x - 4)} + \frac{3 (x - 4)}{(x + 1) (x - 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 (x + 1) + 3 (x - 4)}{(x + 1) (x - 4)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $3$ out of $6 (x + 1) + 3 (x - 4)$ .

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Step 5.1.1

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

$\frac{3 (2 (x + 1)) + 3 (x - 4)}{(x + 1) (x - 4)}$

Step 5.1.2

Factor $3$ out of $3 (2 (x + 1)) + 3 (x - 4)$ .

$\frac{3 (2 (x + 1) + x - 4)}{(x + 1) (x - 4)}$

Step 5.2

Apply the distributive property.

$\frac{3 (2 x + 2 \cdot 1 + x - 4)}{(x + 1) (x - 4)}$

Step 5.3

Multiply $2$ by $1$ .

$\frac{3 (2 x + 2 + x - 4)}{(x + 1) (x - 4)}$

Step 5.4

Add $2 x$ and $x$ .

$\frac{3 (3 x + 2 - 4)}{(x + 1) (x - 4)}$

Step 5.5

Subtract $4$ from $2$ .

$\frac{3 (3 x - 2)}{(x + 1) (x - 4)}$