Algebra Examples

$\frac{6 x - 3 y}{9} - \frac{4 x - 7 y}{2}$

Step 1

Cancel the common factor of $6 x - 3 y$ and $9$ .

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Step 1.1

Factor $3$ out of $6 x$ .

$\frac{3 (2 x) - 3 y}{9} - \frac{4 x - 7 y}{2}$

Step 1.2

Factor $3$ out of $- 3 y$ .

$\frac{3 (2 x) + 3 (- y)}{9} - \frac{4 x - 7 y}{2}$

Step 1.3

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

$\frac{3 (2 x - y)}{9} - \frac{4 x - 7 y}{2}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $3$ out of $9$ .

$\frac{3 (2 x - y)}{3 (3)} - \frac{4 x - 7 y}{2}$

Step 1.4.2

Cancel the common factor.

$\frac{3 (2 x - y)}{3 \cdot 3} - \frac{4 x - 7 y}{2}$

Step 1.4.3

Rewrite the expression.

$\frac{2 x - y}{3} - \frac{4 x - 7 y}{2}$

Step 2

To write $\frac{2 x - y}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x - y}{3} \cdot \frac{2}{2} - \frac{4 x - 7 y}{2}$

Step 3

To write $- \frac{4 x - 7 y}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x - y}{3} \cdot \frac{2}{2} - \frac{4 x - 7 y}{2} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2 x - y}{3}$ by $\frac{2}{2}$ .

$\frac{(2 x - y) \cdot 2}{3 \cdot 2} - \frac{4 x - 7 y}{2} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{(2 x - y) \cdot 2}{6} - \frac{4 x - 7 y}{2} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{4 x - 7 y}{2}$ by $\frac{3}{3}$ .

$\frac{(2 x - y) \cdot 2}{6} - \frac{(4 x - 7 y) \cdot 3}{2 \cdot 3}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{(2 x - y) \cdot 2}{6} - \frac{(4 x - 7 y) \cdot 3}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{(2 x - y) \cdot 2 - (4 x - 7 y) \cdot 3}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{2 x \cdot 2 - y \cdot 2 - (4 x - 7 y) \cdot 3}{6}$

Step 6.2

Multiply $2$ by $2$ .

$\frac{4 x - y \cdot 2 - (4 x - 7 y) \cdot 3}{6}$

Step 6.3

Multiply $2$ by $- 1$ .

$\frac{4 x - 2 y - (4 x - 7 y) \cdot 3}{6}$

Step 6.4

Apply the distributive property.

$\frac{4 x - 2 y + (- (4 x) - (- 7 y)) \cdot 3}{6}$

Step 6.5

Multiply $4$ by $- 1$ .

$\frac{4 x - 2 y + (- 4 x - (- 7 y)) \cdot 3}{6}$

Step 6.6

Multiply $- 7$ by $- 1$ .

$\frac{4 x - 2 y + (- 4 x + 7 y) \cdot 3}{6}$

Step 6.7

Apply the distributive property.

$\frac{4 x - 2 y - 4 x \cdot 3 + 7 y \cdot 3}{6}$

Step 6.8

Multiply $3$ by $- 4$ .

$\frac{4 x - 2 y - 12 x + 7 y \cdot 3}{6}$

Step 6.9

Multiply $3$ by $7$ .

$\frac{4 x - 2 y - 12 x + 21 y}{6}$

Step 6.10

Subtract $12 x$ from $4 x$ .

$\frac{- 8 x - 2 y + 21 y}{6}$

Step 6.11

Add $- 2 y$ and $21 y$ .

$\frac{- 8 x + 19 y}{6}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 8 x$ .

$\frac{- (8 x) + 19 y}{6}$

Step 7.2

Factor $- 1$ out of $19 y$ .

$\frac{- (8 x) - (- 19 y)}{6}$

Step 7.3

Factor $- 1$ out of $- (8 x) - (- 19 y)$ .

$\frac{- (8 x - 19 y)}{6}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (8 x - 19 y)$ as $- 1 (8 x - 19 y)$ .

$\frac{- 1 (8 x - 19 y)}{6}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{8 x - 19 y}{6}$