Algebra Examples

$\frac{2 x - 5}{x} - \frac{4}{5 x} - 4$

Step 1

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

$\frac{2 x - 5}{x} \cdot \frac{5}{5} - \frac{4}{5 x} - 4$

Step 2

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

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Step 2.1

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

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

Step 2.2

Move $5$ to the left of $x$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{2 x \cdot 5 - 5 \cdot 5 - 4}{5 x} - 4$

Step 4.2

Multiply $5$ by $2$ .

$\frac{10 x - 5 \cdot 5 - 4}{5 x} - 4$

Step 4.3

Multiply $- 5$ by $5$ .

$\frac{10 x - 25 - 4}{5 x} - 4$

Step 4.4

Subtract $4$ from $- 25$ .

$\frac{10 x - 29}{5 x} - 4$

Step 5

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

$\frac{10 x - 29}{5 x} - 4 \cdot \frac{5 x}{5 x}$

Step 6

Simplify terms.

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Step 6.1

Combine $- 4$ and $\frac{5 x}{5 x}$ .

$\frac{10 x - 29}{5 x} + \frac{- 4 (5 x)}{5 x}$

Step 6.2

Combine the numerators over the common denominator.

$\frac{10 x - 29 - 4 (5 x)}{5 x}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 4$ by $5$ .

$\frac{10 x - 29 - 20 x}{5 x}$

Step 7.2

Subtract $20 x$ from $10 x$ .

$\frac{- 10 x - 29}{5 x}$

Step 8

Simplify with factoring out.

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Step 8.1

Factor $- 1$ out of $- 10 x$ .

$\frac{- (10 x) - 29}{5 x}$

Step 8.2

Rewrite $- 29$ as $- 1 (29)$ .

$\frac{- (10 x) - 1 (29)}{5 x}$

Step 8.3

Factor $- 1$ out of $- (10 x) - 1 (29)$ .

$\frac{- (10 x + 29)}{5 x}$

Step 8.4

Simplify the expression.

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Step 8.4.1

Rewrite $- (10 x + 29)$ as $- 1 (10 x + 29)$ .

$\frac{- 1 (10 x + 29)}{5 x}$

Step 8.4.2

Move the negative in front of the fraction.

$- \frac{10 x + 29}{5 x}$