Pre-Algebra Examples

$\frac{3 x}{x + 7} + \frac{- 4 x}{x - 7}$

Step 1

Move the negative in front of the fraction.

$\frac{3 x}{x + 7} - \frac{4 x}{x - 7}$

Step 2

To write $\frac{3 x}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{x - 7}{x - 7}$ .

$\frac{3 x}{x + 7} \cdot \frac{x - 7}{x - 7} - \frac{4 x}{x - 7}$

Step 3

To write $- \frac{4 x}{x - 7}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$\frac{3 x}{x + 7} \cdot \frac{x - 7}{x - 7} - \frac{4 x}{x - 7} \cdot \frac{x + 7}{x + 7}$

Step 4

Write each expression with a common denominator of $(x + 7) (x - 7)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3 x}{x + 7}$ by $\frac{x - 7}{x - 7}$ .

$\frac{3 x (x - 7)}{(x + 7) (x - 7)} - \frac{4 x}{x - 7} \cdot \frac{x + 7}{x + 7}$

Step 4.2

Multiply $\frac{4 x}{x - 7}$ by $\frac{x + 7}{x + 7}$ .

$\frac{3 x (x - 7)}{(x + 7) (x - 7)} - \frac{4 x (x + 7)}{(x - 7) (x + 7)}$

Step 4.3

Reorder the factors of $(x - 7) (x + 7)$ .

$\frac{3 x (x - 7)}{(x + 7) (x - 7)} - \frac{4 x (x + 7)}{(x + 7) (x - 7)}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 x (x - 7) - 4 x (x + 7)}{(x + 7) (x - 7)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $x$ out of $3 x (x - 7) - 4 x (x + 7)$ .

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Step 6.1.1

Factor $x$ out of $3 x (x - 7)$ .

$\frac{x (3 (x - 7)) - 4 x (x + 7)}{(x + 7) (x - 7)}$

Step 6.1.2

Factor $x$ out of $- 4 x (x + 7)$ .

$\frac{x (3 (x - 7)) + x (- 4 (x + 7))}{(x + 7) (x - 7)}$

Step 6.1.3

Factor $x$ out of $x (3 (x - 7)) + x (- 4 (x + 7))$ .

$\frac{x (3 (x - 7) - 4 (x + 7))}{(x + 7) (x - 7)}$

Step 6.2

Apply the distributive property.

$\frac{x (3 x + 3 \cdot - 7 - 4 (x + 7))}{(x + 7) (x - 7)}$

Step 6.3

Multiply $3$ by $- 7$ .

$\frac{x (3 x - 21 - 4 (x + 7))}{(x + 7) (x - 7)}$

Step 6.4

Apply the distributive property.

$\frac{x (3 x - 21 - 4 x - 4 \cdot 7)}{(x + 7) (x - 7)}$

Step 6.5

Multiply $- 4$ by $7$ .

$\frac{x (3 x - 21 - 4 x - 28)}{(x + 7) (x - 7)}$

Step 6.6

Subtract $4 x$ from $3 x$ .

$\frac{x (- x - 21 - 28)}{(x + 7) (x - 7)}$

Step 6.7

Subtract $28$ from $- 21$ .

$\frac{x (- x - 49)}{(x + 7) (x - 7)}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- x$ .

$\frac{x (- (x) - 49)}{(x + 7) (x - 7)}$

Step 7.2

Rewrite $- 49$ as $- 1 (49)$ .

$\frac{x (- (x) - 1 (49))}{(x + 7) (x - 7)}$

Step 7.3

Factor $- 1$ out of $- (x) - 1 (49)$ .

$\frac{x (- (x + 49))}{(x + 7) (x - 7)}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (x + 49)$ as $- 1 (x + 49)$ .

$\frac{x (- 1 (x + 49))}{(x + 7) (x - 7)}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{x (x + 49)}{(x + 7) (x - 7)}$