Algebra Examples

$\frac{5 + \frac{5}{x - 1}}{\frac{5}{x - 1}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(5 + \frac{5}{x - 1}) \frac{x - 1}{5}$

Step 2

To write $5$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$(\frac{5 (x - 1)}{x - 1} + \frac{5}{x - 1}) \frac{x - 1}{5}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 (x - 1) + 5}{x - 1} \cdot \frac{x - 1}{5}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $5$ out of $5 (x - 1) + 5$ .

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Step 4.1.1

Factor $5$ out of $5$ .

$\frac{5 (x - 1) + 5 (1)}{x - 1} \cdot \frac{x - 1}{5}$

Step 4.1.2

Factor $5$ out of $5 (x - 1) + 5 (1)$ .

$\frac{5 (x - 1 + 1)}{x - 1} \cdot \frac{x - 1}{5}$

Step 4.2

Add $- 1$ and $1$ .

$\frac{5 (x + 0)}{x - 1} \cdot \frac{x - 1}{5}$

Step 4.3

Add $x$ and $0$ .

$\frac{5 x}{x - 1} \cdot \frac{x - 1}{5}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $5$ .

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Step 5.1.1

Factor $5$ out of $5 x$ .

$\frac{5 (x)}{x - 1} \cdot \frac{x - 1}{5}$

Step 5.1.2

Cancel the common factor.

$\frac{5 x}{x - 1} \cdot \frac{x - 1}{5}$

Step 5.1.3

Rewrite the expression.

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

Step 5.2

Cancel the common factor of $x - 1$ .

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Step 5.2.1

Cancel the common factor.

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

Step 5.2.2

Rewrite the expression.

$x$