Linear Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Rewrite $7$ as $- 1 (- 7)$ .

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

Step 1.2

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

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

Step 1.3

Factor $- 1$ out of $- 1 (- 7) - (x)$ .

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

Step 1.4

Simplify the expression.

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Step 1.4.1

Move a negative from the denominator of $\frac{3 x}{- 1 (- 7 + x)}$ to the numerator.

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

Step 1.4.2

Reorder terms.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1$ by $3$ .

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

Step 2.2

Subtract $3 x$ from $7 x$ .

$\frac{4 x + 8}{x - 7}$

Step 2.3

Factor $4$ out of $4 x + 8$ .

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Step 2.3.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) + 8}{x - 7}$

Step 2.3.2

Factor $4$ out of $8$ .

$\frac{4 x + 4 \cdot 2}{x - 7}$

Step 2.3.3

Factor $4$ out of $4 x + 4 \cdot 2$ .

$\frac{4 (x + 2)}{x - 7}$