Algebra Examples

$\frac{\frac{6}{x - 1} - 3}{\frac{3}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{6}{x - 1} - 3) \frac{x}{3}$

Step 2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$(\frac{6}{x - 1} - 3 \cdot \frac{x - 1}{x - 1}) \frac{x}{3}$

Step 3

Simplify terms.

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Step 3.1

Combine $- 3$ and $\frac{x - 1}{x - 1}$ .

$(\frac{6}{x - 1} + \frac{- 3 (x - 1)}{x - 1}) \frac{x}{3}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{6 - 3 (x - 1)}{x - 1} \cdot \frac{x}{3}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $3$ out of $6 - 3 (x - 1)$ .

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Step 4.1.1

Factor $3$ out of $6$ .

$\frac{3 (2) - 3 (x - 1)}{x - 1} \cdot \frac{x}{3}$

Step 4.1.2

Factor $3$ out of $- 3 (x - 1)$ .

$\frac{3 (2) + 3 (- (x - 1))}{x - 1} \cdot \frac{x}{3}$

Step 4.1.3

Factor $3$ out of $3 (2) + 3 (- (x - 1))$ .

$\frac{3 (2 - (x - 1))}{x - 1} \cdot \frac{x}{3}$

Step 4.2

Apply the distributive property.

$\frac{3 (2 - x - - 1)}{x - 1} \cdot \frac{x}{3}$

Step 4.3

Multiply $- 1$ by $- 1$ .

$\frac{3 (2 - x + 1)}{x - 1} \cdot \frac{x}{3}$

Step 4.4

Add $2$ and $1$ .

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

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Cancel the common factor.

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

Step 5.1.2

Rewrite the expression.

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

Step 5.2

Combine $\frac{- x + 3}{x - 1}$ and $x$ .

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

Step 5.3

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

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

Step 5.4

Rewrite $3$ as $- 1 (- 3)$ .

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

Step 5.5

Factor $- 1$ out of $- (x) - 1 (- 3)$ .

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

Step 5.6

Simplify the expression.

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Step 5.6.1

Rewrite $- (x - 3)$ as $- 1 (x - 3)$ .

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

Step 5.6.2

Move the negative in front of the fraction.

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

Step 5.6.3

Reorder factors in $- \frac{(x - 3) x}{x - 1}$ .

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