Simplify 6/7x-2/5y+5/7(y+x)

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

Step 1

Simplify each term.

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

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

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

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

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

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

Apply the distributive property.

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

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

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

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.

Combine the numerators over the common denominator.

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

Add $6 x$ and $5 x$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

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 5

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 6

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

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

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

Multiply $7$ by $5$ .

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

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

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

Multiply $5$ by $7$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Simplify the numerator.

Apply the distributive property.

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

Multiply $5$ by $11$ .

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

Multiply $5$ by $5$ .

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

Multiply $7$ by $- 2$ .

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

Subtract $14 y$ from $25 y$ .

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

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

Factor $11$ out of $55 x$ .

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

Factor $11$ out of $11 y$ .

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

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

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

Simplify 6/7x-2/5y+5/7(y+x)

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