Algebra Examples

$\frac{\frac{2}{x - 1} + \frac{1}{x}}{\frac{8}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{2}{x - 1} + \frac{1}{x}) \frac{x}{8}$

Step 2

To write $\frac{2}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$(\frac{2}{x - 1} \cdot \frac{x}{x} + \frac{1}{x}) \frac{x}{8}$

Step 3

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

$(\frac{2}{x - 1} \cdot \frac{x}{x} + \frac{1}{x} \cdot \frac{x - 1}{x - 1}) \frac{x}{8}$

Step 4

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

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Step 4.1

Multiply $\frac{2}{x - 1}$ by $\frac{x}{x}$ .

$(\frac{2 x}{(x - 1) x} + \frac{1}{x} \cdot \frac{x - 1}{x - 1}) \frac{x}{8}$

Step 4.2

Multiply $\frac{1}{x}$ by $\frac{x - 1}{x - 1}$ .

$(\frac{2 x}{(x - 1) x} + \frac{x - 1}{x (x - 1)}) \frac{x}{8}$

Step 4.3

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

$(\frac{2 x}{x (x - 1)} + \frac{x - 1}{x (x - 1)}) \frac{x}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 x + x - 1}{x (x - 1)} \cdot \frac{x}{8}$

Step 6

Add $2 x$ and $x$ .

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

Step 7

Simplify terms.

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Step 7.1

Cancel the common factor of $x$ .

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Step 7.1.1

Cancel the common factor.

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

Step 7.1.2

Rewrite the expression.

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

Step 7.2

Multiply $\frac{3 x - 1}{x - 1}$ by $\frac{1}{8}$ .

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

Step 7.3

Move $8$ to the left of $x - 1$ .

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