Algebra Examples

$\frac{3 x}{8 - x} + \frac{7 x + 1}{x - 8}$

Step 1

Simplify terms.

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Step 1.1

Factor $- 1$ out of $x$ .

$\frac{3 x}{8 - x} + \frac{7 x + 1}{- 1 (- x) - 8}$

Step 1.2

Rewrite $- 8$ as $- 1 (8)$ .

$\frac{3 x}{8 - x} + \frac{7 x + 1}{- 1 (- x) - 1 (8)}$

Step 1.3

Factor $- 1$ out of $- 1 (- x) - 1 (8)$ .

$\frac{3 x}{8 - x} + \frac{7 x + 1}{- 1 (- x + 8)}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{7 x + 1}{- 1 (- x + 8)}$ to the numerator.

$\frac{3 x}{8 - x} + \frac{- (7 x + 1)}{- x + 8}$

Step 1.4.2

Reorder terms.

$\frac{3 x}{- x + 8} + \frac{- (7 x + 1)}{- x + 8}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 x - (7 x + 1)}{- x + 8}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

$\frac{3 x - (7 x) - 1 \cdot 1}{- x + 8}$

Step 2.2

Multiply $7$ by $- 1$ .

$\frac{3 x - 7 x - 1 \cdot 1}{- x + 8}$

Step 2.3

Multiply $- 1$ by $1$ .

$\frac{3 x - 7 x - 1}{- x + 8}$

Step 2.4

Subtract $7 x$ from $3 x$ .

$\frac{- 4 x - 1}{- x + 8}$

Step 3

Simplify terms.

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Step 3.1

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) - 1}{- x + 8}$

Step 3.2

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

$\frac{- (4 x) - 1 (1)}{- x + 8}$

Step 3.3

Factor $- 1$ out of $- (4 x) - 1 (1)$ .

$\frac{- (4 x + 1)}{- x + 8}$

Step 3.4

Rewrite $- (4 x + 1)$ as $- 1 (4 x + 1)$ .

$\frac{- 1 (4 x + 1)}{- x + 8}$

Step 3.5

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

$\frac{- 1 (4 x + 1)}{- (x) + 8}$

Step 3.6

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{- 1 (4 x + 1)}{- (x) - 1 (- 8)}$

Step 3.7

Factor $- 1$ out of $- (x) - 1 (- 8)$ .

$\frac{- 1 (4 x + 1)}{- (x - 8)}$

Step 3.8

Rewrite $- (x - 8)$ as $- 1 (x - 8)$ .

$\frac{- 1 (4 x + 1)}{- 1 (x - 8)}$

Step 3.9

Cancel the common factor.

$\frac{- 1 (4 x + 1)}{- 1 (x - 8)}$

Step 3.10

Rewrite the expression.

$\frac{4 x + 1}{x - 8}$