Algebra Examples

$\frac{\frac{1}{2 x - 5} - \frac{7}{8 x - 20}}{\frac{x}{2 x - 5}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{1}{2 x - 5} - \frac{7}{8 x - 20}) \frac{2 x - 5}{x}$

Step 2

Factor $4$ out of $8 x - 20$ .

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Step 2.1

Factor $4$ out of $8 x$ .

$(\frac{1}{2 x - 5} - \frac{7}{4 (2 x) - 20}) \frac{2 x - 5}{x}$

Step 2.2

Factor $4$ out of $- 20$ .

$(\frac{1}{2 x - 5} - \frac{7}{4 (2 x) + 4 (- 5)}) \frac{2 x - 5}{x}$

Step 2.3

Factor $4$ out of $4 (2 x) + 4 (- 5)$ .

$(\frac{1}{2 x - 5} - \frac{7}{4 (2 x - 5)}) \frac{2 x - 5}{x}$

Step 3

To write $\frac{1}{2 x - 5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{1}{2 x - 5} \cdot \frac{4}{4} - \frac{7}{4 (2 x - 5)}) \frac{2 x - 5}{x}$

Step 4

Write each expression with a common denominator of $(2 x - 5) \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{2 x - 5}$ by $\frac{4}{4}$ .

$(\frac{4}{(2 x - 5) \cdot 4} - \frac{7}{4 (2 x - 5)}) \frac{2 x - 5}{x}$

Step 4.2

Reorder the factors of $(2 x - 5) \cdot 4$ .

$(\frac{4}{4 (2 x - 5)} - \frac{7}{4 (2 x - 5)}) \frac{2 x - 5}{x}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 - 7}{4 (2 x - 5)} \cdot \frac{2 x - 5}{x}$

Step 6

Subtract $7$ from $4$ .

$\frac{- 3}{4 (2 x - 5)} \cdot \frac{2 x - 5}{x}$

Step 7

Cancel the common factor of $2 x - 5$ .

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Step 7.1

Factor $2 x - 5$ out of $4 (2 x - 5)$ .

$\frac{- 3}{(2 x - 5) \cdot 4} \cdot \frac{2 x - 5}{x}$

Step 7.2

Cancel the common factor.

$\frac{- 3}{(2 x - 5) \cdot 4} \cdot \frac{2 x - 5}{x}$

Step 7.3

Rewrite the expression.

$\frac{- 3}{4} \cdot \frac{1}{x}$

Step 8

Multiply $\frac{- 3}{4}$ by $\frac{1}{x}$ .

$\frac{- 3}{4 x}$

Step 9

Move the negative in front of the fraction.

$- \frac{3}{4 x}$