Simplify y-((3y-7)/7)÷(8/35)+2/(5y)

$y - \frac{3 y - 7}{7} \div \frac{8}{35} + \frac{2}{5 y}$

Step 1

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$y - (\frac{3 y - 7}{7} \cdot \frac{35}{8}) + \frac{2}{5 y}$

Cancel the common factor of $7$ .

Factor $7$ out of $35$ .

$y - (\frac{3 y - 7}{7} \cdot \frac{7 (5)}{8}) + \frac{2}{5 y}$

Cancel the common factor.

$y - (\frac{3 y - 7}{7} \cdot \frac{7 \cdot 5}{8}) + \frac{2}{5 y}$

Rewrite the expression.

$y - ((3 y - 7) \frac{5}{8}) + \frac{2}{5 y}$

Apply the distributive property.

$y - (3 y \frac{5}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Multiply $3 y \frac{5}{8}$ .

Combine $3$ and $\frac{5}{8}$ .

$y - (y \frac{3 \cdot 5}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Multiply $3$ by $5$ .

$y - (y \frac{15}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Combine $y$ and $\frac{15}{8}$ .

$y - (\frac{y \cdot 15}{8} - 7 (\frac{5}{8})) + \frac{2}{5 y}$

Multiply $- 7 (\frac{5}{8})$ .

Combine $- 7$ and $\frac{5}{8}$ .

$y - (\frac{y \cdot 15}{8} + \frac{- 7 \cdot 5}{8}) + \frac{2}{5 y}$

Multiply $- 7$ by $5$ .

$y - (\frac{y \cdot 15}{8} + \frac{- 35}{8}) + \frac{2}{5 y}$

Combine the numerators over the common denominator.

$y - \frac{y \cdot 15 - 35}{8} + \frac{2}{5 y}$

Reorder factors in $y \cdot 15 - 35$ .

$y - \frac{15 y - 35}{8} + \frac{2}{5 y}$

Factor $5$ out of $15 y - 35$ .

Factor $5$ out of $15 y$ .

$y - \frac{5 (3 y) - 35}{8} + \frac{2}{5 y}$

Factor $5$ out of $- 35$ .

$y - \frac{5 (3 y) + 5 (- 7)}{8} + \frac{2}{5 y}$

Factor $5$ out of $5 (3 y) + 5 (- 7)$ .

$y - \frac{5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 2

To write $y$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y \cdot \frac{8}{8} - \frac{5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 3

Simplify terms.

Combine $y$ and $\frac{8}{8}$ .

$\frac{y \cdot 8}{8} - \frac{5 (3 y - 7)}{8} + \frac{2}{5 y}$

Combine the numerators over the common denominator.

$\frac{y \cdot 8 - 5 (3 y - 7)}{8} + \frac{2}{5 y}$

Step 4

Simplify the numerator.

Move $8$ to the left of $y$ .

$\frac{8 \cdot y - 5 (3 y - 7)}{8} + \frac{2}{5 y}$

Apply the distributive property.

$\frac{8 y - 5 (3 y) - 5 \cdot - 7}{8} + \frac{2}{5 y}$

Multiply $3$ by $- 5$ .

$\frac{8 y - 15 y - 5 \cdot - 7}{8} + \frac{2}{5 y}$

Multiply $- 5$ by $- 7$ .

$\frac{8 y - 15 y + 35}{8} + \frac{2}{5 y}$

Subtract $15 y$ from $8 y$ .

$\frac{- 7 y + 35}{8} + \frac{2}{5 y}$

Factor $7$ out of $- 7 y + 35$ .

Factor $7$ out of $- 7 y$ .

$\frac{7 (- y) + 35}{8} + \frac{2}{5 y}$

Factor $7$ out of $35$ .

$\frac{7 (- y) + 7 (5)}{8} + \frac{2}{5 y}$

Factor $7$ out of $7 (- y) + 7 (5)$ .

$\frac{7 (- y + 5)}{8} + \frac{2}{5 y}$

Step 5

To write $\frac{7 (- y + 5)}{8}$ as a fraction with a common denominator, multiply by $\frac{5 y}{5 y}$ .

$\frac{7 (- y + 5)}{8} \cdot \frac{5 y}{5 y} + \frac{2}{5 y}$

Step 6

To write $\frac{2}{5 y}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{7 (- y + 5)}{8} \cdot \frac{5 y}{5 y} + \frac{2}{5 y} \cdot \frac{8}{8}$

Step 7

Write each expression with a common denominator of $40 y$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7 (- y + 5)}{8}$ by $\frac{5 y}{5 y}$ .

$\frac{7 (- y + 5) (5 y)}{8 (5 y)} + \frac{2}{5 y} \cdot \frac{8}{8}$

Multiply $5$ by $8$ .

$\frac{7 (- y + 5) (5 y)}{40 y} + \frac{2}{5 y} \cdot \frac{8}{8}$

Multiply $\frac{2}{5 y}$ by $\frac{8}{8}$ .

$\frac{7 (- y + 5) (5 y)}{40 y} + \frac{2 \cdot 8}{5 y \cdot 8}$

Multiply $8$ by $5$ .

$\frac{7 (- y + 5) (5 y)}{40 y} + \frac{2 \cdot 8}{40 y}$

Step 8

Combine the numerators over the common denominator.

$\frac{7 (- y + 5) (5 y) + 2 \cdot 8}{40 y}$

Step 9

Simplify the numerator.

Apply the distributive property.

$\frac{(7 (- y) + 7 \cdot 5) (5 y) + 2 \cdot 8}{40 y}$

Multiply $- 1$ by $7$ .

$\frac{(- 7 y + 7 \cdot 5) (5 y) + 2 \cdot 8}{40 y}$

Multiply $7$ by $5$ .

$\frac{(- 7 y + 35) (5 y) + 2 \cdot 8}{40 y}$

Apply the distributive property.

$\frac{- 7 y (5 y) + 35 (5 y) + 2 \cdot 8}{40 y}$

Rewrite using the commutative property of multiplication.

$\frac{- 7 \cdot 5 y \cdot y + 35 (5 y) + 2 \cdot 8}{40 y}$

Multiply $5$ by $35$ .

$\frac{- 7 \cdot 5 y \cdot y + 175 y + 2 \cdot 8}{40 y}$

Simplify each term.

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{- 7 \cdot 5 (y \cdot y) + 175 y + 2 \cdot 8}{40 y}$

Multiply $y$ by $y$ .

$\frac{- 7 \cdot 5 y^{2} + 175 y + 2 \cdot 8}{40 y}$

Multiply $- 7$ by $5$ .

$\frac{- 35 y^{2} + 175 y + 2 \cdot 8}{40 y}$

Multiply $2$ by $8$ .

$\frac{- 35 y^{2} + 175 y + 16}{40 y}$

Step 10

Simplify with factoring out.

Factor $- 1$ out of $- 35 y^{2}$ .

$\frac{- (35 y^{2}) + 175 y + 16}{40 y}$

Factor $- 1$ out of $175 y$ .

$\frac{- (35 y^{2}) - (- 175 y) + 16}{40 y}$

Factor $- 1$ out of $- (35 y^{2}) - (- 175 y)$ .

$\frac{- (35 y^{2} - 175 y) + 16}{40 y}$

Rewrite $16$ as $- 1 (- 16)$ .

$\frac{- (35 y^{2} - 175 y) - 1 (- 16)}{40 y}$

Factor $- 1$ out of $- (35 y^{2} - 175 y) - 1 (- 16)$ .

$\frac{- (35 y^{2} - 175 y - 16)}{40 y}$

Simplify the expression.

Rewrite $- (35 y^{2} - 175 y - 16)$ as $- 1 (35 y^{2} - 175 y - 16)$ .

$\frac{- 1 (35 y^{2} - 175 y - 16)}{40 y}$

Move the negative in front of the fraction.

$- \frac{35 y^{2} - 175 y - 16}{40 y}$

Simplify y-((3y-7)/7)÷(8/35)+2/(5y)

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