Algebra Examples

$\frac{6}{7} x - \frac{2}{5} y + \frac{5}{7} (y + x)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{6}{7}$ and $x$ .

$\frac{6 x}{7} - \frac{2}{5} y + \frac{5}{7} \cdot (y + x)$

Step 1.2

Combine $y$ and $\frac{2}{5}$ .

$\frac{6 x}{7} - \frac{y \cdot 2}{5} + \frac{5}{7} \cdot (y + x)$

Step 1.3

Move $2$ to the left of $y$ .

$\frac{6 x}{7} - \frac{2 \cdot y}{5} + \frac{5}{7} \cdot (y + x)$

Step 1.4

Apply the distributive property.

$\frac{6 x}{7} - \frac{2 y}{5} + \frac{5}{7} y + \frac{5}{7} x$

Step 1.5

Combine $\frac{5}{7}$ and $y$ .

$\frac{6 x}{7} - \frac{2 y}{5} + \frac{5 y}{7} + \frac{5}{7} x$

Step 1.6

Combine $\frac{5}{7}$ and $x$ .

$\frac{6 x}{7} - \frac{2 y}{5} + \frac{5 y}{7} + \frac{5 x}{7}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{6 x + 5 y + 5 x}{7} + \frac{- 2 y}{5}$

Step 2.2

Add $6 x$ and $5 x$ .

$\frac{11 x + 5 y}{7} + \frac{- 2 y}{5}$

Step 2.3

Move the negative in front of the fraction.

$\frac{11 x + 5 y}{7} - \frac{2 y}{5}$

Step 3

To write $\frac{11 x + 5 y}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{11 x + 5 y}{7} \cdot \frac{5}{5} - \frac{2 y}{5}$

Step 4

To write $- \frac{2 y}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{11 x + 5 y}{7} \cdot \frac{5}{5} - \frac{2 y}{5} \cdot \frac{7}{7}$

Step 5

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{11 x + 5 y}{7}$ by $\frac{5}{5}$ .

$\frac{(11 x + 5 y) \cdot 5}{7 \cdot 5} - \frac{2 y}{5} \cdot \frac{7}{7}$

Step 5.2

Multiply $7$ by $5$ .

$\frac{(11 x + 5 y) \cdot 5}{35} - \frac{2 y}{5} \cdot \frac{7}{7}$

Step 5.3

Multiply $\frac{2 y}{5}$ by $\frac{7}{7}$ .

$\frac{(11 x + 5 y) \cdot 5}{35} - \frac{2 y \cdot 7}{5 \cdot 7}$

Step 5.4

Multiply $5$ by $7$ .

$\frac{(11 x + 5 y) \cdot 5}{35} - \frac{2 y \cdot 7}{35}$

Step 6

Combine the numerators over the common denominator.

$\frac{(11 x + 5 y) \cdot 5 - 2 y \cdot 7}{35}$

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$\frac{11 x \cdot 5 + 5 y \cdot 5 - 2 y \cdot 7}{35}$

Step 7.2

Multiply $5$ by $11$ .

$\frac{55 x + 5 y \cdot 5 - 2 y \cdot 7}{35}$

Step 7.3

Multiply $5$ by $5$ .

$\frac{55 x + 25 y - 2 y \cdot 7}{35}$

Step 7.4

Multiply $7$ by $- 2$ .

$\frac{55 x + 25 y - 14 y}{35}$

Step 7.5

Subtract $14 y$ from $25 y$ .

$\frac{55 x + 11 y}{35}$

Step 7.6

Factor $11$ out of $55 x + 11 y$ .

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Step 7.6.1

Factor $11$ out of $55 x$ .

$\frac{11 (5 x) + 11 y}{35}$

Step 7.6.2

Factor $11$ out of $11 y$ .

$\frac{11 (5 x) + 11 (y)}{35}$

Step 7.6.3

Factor $11$ out of $11 (5 x) + 11 (y)$ .

$\frac{11 (5 x + y)}{35}$