Algebra Examples

$\frac{6}{x - 1} - \frac{5 x}{4}$

Step 1

To write $\frac{6}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{6}{x - 1} \cdot \frac{4}{4} - \frac{5 x}{4}$

Step 2

To write $- \frac{5 x}{4}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{6}{x - 1} \cdot \frac{4}{4} - \frac{5 x}{4} \cdot \frac{x - 1}{x - 1}$

Step 3

Write each expression with a common denominator of $(x - 1) \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{x - 1}$ by $\frac{4}{4}$ .

$\frac{6 \cdot 4}{(x - 1) \cdot 4} - \frac{5 x}{4} \cdot \frac{x - 1}{x - 1}$

Step 3.2

Multiply $\frac{5 x}{4}$ by $\frac{x - 1}{x - 1}$ .

$\frac{6 \cdot 4}{(x - 1) \cdot 4} - \frac{5 x (x - 1)}{4 (x - 1)}$

Step 3.3

Reorder the factors of $(x - 1) \cdot 4$ .

$\frac{6 \cdot 4}{4 (x - 1)} - \frac{5 x (x - 1)}{4 (x - 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 \cdot 4 - 5 x (x - 1)}{4 (x - 1)}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $6$ by $4$ .

$\frac{24 - 5 x (x - 1)}{4 (x - 1)}$

Step 5.2

Apply the distributive property.

$\frac{24 - 5 x \cdot x - 5 x \cdot - 1}{4 (x - 1)}$

Step 5.3

Multiply $x$ by $x$ by adding the exponents.

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Step 5.3.1

Move $x$ .

$\frac{24 - 5 (x \cdot x) - 5 x \cdot - 1}{4 (x - 1)}$

Step 5.3.2

Multiply $x$ by $x$ .

$\frac{24 - 5 x^{2} - 5 x \cdot - 1}{4 (x - 1)}$

Step 5.4

Multiply $- 1$ by $- 5$ .

$\frac{24 - 5 x^{2} + 5 x}{4 (x - 1)}$

Step 5.5

Reorder terms.

$\frac{- 5 x^{2} + 5 x + 24}{4 (x - 1)}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- 5 x^{2}$ .

$\frac{- (5 x^{2}) + 5 x + 24}{4 (x - 1)}$

Step 6.2

Factor $- 1$ out of $5 x$ .

$\frac{- (5 x^{2}) - (- 5 x) + 24}{4 (x - 1)}$

Step 6.3

Factor $- 1$ out of $- (5 x^{2}) - (- 5 x)$ .

$\frac{- (5 x^{2} - 5 x) + 24}{4 (x - 1)}$

Step 6.4

Rewrite $24$ as $- 1 (- 24)$ .

$\frac{- (5 x^{2} - 5 x) - 1 (- 24)}{4 (x - 1)}$

Step 6.5

Factor $- 1$ out of $- (5 x^{2} - 5 x) - 1 (- 24)$ .

$\frac{- (5 x^{2} - 5 x - 24)}{4 (x - 1)}$

Step 6.6

Simplify the expression.

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Step 6.6.1

Rewrite $- (5 x^{2} - 5 x - 24)$ as $- 1 (5 x^{2} - 5 x - 24)$ .

$\frac{- 1 (5 x^{2} - 5 x - 24)}{4 (x - 1)}$

Step 6.6.2

Move the negative in front of the fraction.

$- \frac{5 x^{2} - 5 x - 24}{4 (x - 1)}$