Algebra Examples

$\frac{x - 4 y}{5 x} - \frac{4 x}{3 x}$

Step 1

Cancel the common factor of $x$ .

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Step 1.1

Cancel the common factor.

$\frac{x - 4 y}{5 x} - \frac{4 x}{3 x}$

Step 1.2

Rewrite the expression.

$\frac{x - 4 y}{5 x} - \frac{4}{3}$

Step 2

To write $\frac{x - 4 y}{5 x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x - 4 y}{5 x} \cdot \frac{3}{3} - \frac{4}{3}$

Step 3

To write $- \frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{5 x}{5 x}$ .

$\frac{x - 4 y}{5 x} \cdot \frac{3}{3} - \frac{4}{3} \cdot \frac{5 x}{5 x}$

Step 4

Write each expression with a common denominator of $15 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x - 4 y}{5 x}$ by $\frac{3}{3}$ .

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

Step 4.2

Multiply $3$ by $5$ .

$\frac{(x - 4 y) \cdot 3}{15 x} - \frac{4}{3} \cdot \frac{5 x}{5 x}$

Step 4.3

Multiply $\frac{4}{3}$ by $\frac{5 x}{5 x}$ .

$\frac{(x - 4 y) \cdot 3}{15 x} - \frac{4 (5 x)}{3 (5 x)}$

Step 4.4

Multiply $5$ by $3$ .

$\frac{(x - 4 y) \cdot 3}{15 x} - \frac{4 (5 x)}{15 x}$

Step 5

Combine the numerators over the common denominator.

$\frac{(x - 4 y) \cdot 3 - 4 (5 x)}{15 x}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{x \cdot 3 - 4 y \cdot 3 - 4 \cdot 5 x}{15 x}$

Step 6.2

Move $3$ to the left of $x$ .

$\frac{3 \cdot x - 4 y \cdot 3 - 4 \cdot 5 x}{15 x}$

Step 6.3

Multiply $3$ by $- 4$ .

$\frac{3 \cdot x - 12 y - 4 \cdot 5 x}{15 x}$

Step 6.4

Multiply $- 4$ by $5$ .

$\frac{3 x - 12 y - 20 x}{15 x}$

Step 6.5

Subtract $20 x$ from $3 x$ .

$\frac{- 17 x - 12 y}{15 x}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 17 x$ .

$\frac{- (17 x) - 12 y}{15 x}$

Step 7.2

Factor $- 1$ out of $- 12 y$ .

$\frac{- (17 x) - (12 y)}{15 x}$

Step 7.3

Factor $- 1$ out of $- (17 x) - (12 y)$ .

$\frac{- (17 x + 12 y)}{15 x}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (17 x + 12 y)$ as $- 1 (17 x + 12 y)$ .

$\frac{- 1 (17 x + 12 y)}{15 x}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{17 x + 12 y}{15 x}$