Simplify (2x-7y)/(2x^2y)-(5y-8x)/(5xy^2)

$\frac{2 x - 7 y}{2 x^{2} y} - \frac{5 y - 8 x}{5 x y^{2}}$

Step 1

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

$\frac{2 x - 7 y}{2 x^{2} y} \cdot \frac{5 y}{5 y} - \frac{5 y - 8 x}{5 x y^{2}}$

Step 2

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

$\frac{2 x - 7 y}{2 x^{2} y} \cdot \frac{5 y}{5 y} - \frac{5 y - 8 x}{5 x y^{2}} \cdot \frac{2 x}{2 x}$

Step 3

Write each expression with a common denominator of $10 x^{2} y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $2$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y \cdot y} - \frac{5 y - 8 x}{5 x y^{2}} \cdot \frac{2 x}{2 x}$

Raise $y$ to the power of $1$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} (y^{1} y)} - \frac{5 y - 8 x}{5 x y^{2}} \cdot \frac{2 x}{2 x}$

Raise $y$ to the power of $1$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} (y^{1} y^{1})} - \frac{5 y - 8 x}{5 x y^{2}} \cdot \frac{2 x}{2 x}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{1 + 1}} - \frac{5 y - 8 x}{5 x y^{2}} \cdot \frac{2 x}{2 x}$

Add $1$ and $1$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{2}} - \frac{5 y - 8 x}{5 x y^{2}} \cdot \frac{2 x}{2 x}$

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

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{2}} - \frac{(5 y - 8 x) (2 x)}{5 x y^{2} (2 x)}$

Multiply $2$ by $5$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{2}} - \frac{(5 y - 8 x) (2 x)}{10 x y^{2} x}$

Raise $x$ to the power of $1$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{2}} - \frac{(5 y - 8 x) (2 x)}{10 (x^{1} x) y^{2}}$

Raise $x$ to the power of $1$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{2}} - \frac{(5 y - 8 x) (2 x)}{10 (x^{1} x^{1}) y^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{2}} - \frac{(5 y - 8 x) (2 x)}{10 x^{1 + 1} y^{2}}$

Add $1$ and $1$ .

$\frac{(2 x - 7 y) (5 y)}{10 x^{2} y^{2}} - \frac{(5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{(2 x - 7 y) (5 y) - (5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{(2 x \cdot 5 - 7 y \cdot 5) y - (5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

Multiply $5$ by $2$ .

$\frac{(10 x - 7 y \cdot 5) y - (5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

Multiply $5$ by $- 7$ .

$\frac{(10 x - 35 y) y - (5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

Apply the distributive property.

$\frac{10 x y - 35 y \cdot y - (5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

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

Move $y$ .

$\frac{10 x y - 35 (y \cdot y) - (5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

Multiply $y$ by $y$ .

$\frac{10 x y - 35 y^{2} - (5 y - 8 x) (2 x)}{10 x^{2} y^{2}}$

Apply the distributive property.

$\frac{10 x y - 35 y^{2} + (- (5 y) - (- 8 x)) (2 x)}{10 x^{2} y^{2}}$

Multiply $5$ by $- 1$ .

$\frac{10 x y - 35 y^{2} + (- 5 y - (- 8 x)) (2 x)}{10 x^{2} y^{2}}$

Multiply $- 8$ by $- 1$ .

$\frac{10 x y - 35 y^{2} + (- 5 y + 8 x) (2 x)}{10 x^{2} y^{2}}$

Apply the distributive property.

$\frac{10 x y - 35 y^{2} - 5 y (2 x) + 8 x (2 x)}{10 x^{2} y^{2}}$

Rewrite using the commutative property of multiplication.

$\frac{10 x y - 35 y^{2} - 5 \cdot 2 y x + 8 x (2 x)}{10 x^{2} y^{2}}$

Rewrite using the commutative property of multiplication.

$\frac{10 x y - 35 y^{2} - 5 \cdot 2 y x + 8 \cdot 2 x \cdot x}{10 x^{2} y^{2}}$

Simplify each term.

Multiply $- 5$ by $2$ .

$\frac{10 x y - 35 y^{2} - 10 y x + 8 \cdot 2 x \cdot x}{10 x^{2} y^{2}}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{10 x y - 35 y^{2} - 10 y x + 8 \cdot 2 (x \cdot x)}{10 x^{2} y^{2}}$

Multiply $x$ by $x$ .

$\frac{10 x y - 35 y^{2} - 10 y x + 8 \cdot 2 x^{2}}{10 x^{2} y^{2}}$

Multiply $8$ by $2$ .

$\frac{10 x y - 35 y^{2} - 10 y x + 16 x^{2}}{10 x^{2} y^{2}}$

Subtract $10 y x$ from $10 x y$ .

Move $y$ .

$\frac{- 35 y^{2} + 10 x y - 10 x y + 16 x^{2}}{10 x^{2} y^{2}}$

Subtract $10 x y$ from $10 x y$ .

$\frac{- 35 y^{2} + 0 + 16 x^{2}}{10 x^{2} y^{2}}$

Add $- 35 y^{2}$ and $0$ .

$\frac{- 35 y^{2} + 16 x^{2}}{10 x^{2} y^{2}}$

Step 6

Simplify with factoring out.

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

$\frac{- (35 y^{2}) + 16 x^{2}}{10 x^{2} y^{2}}$

Factor $- 1$ out of $16 x^{2}$ .

$\frac{- (35 y^{2}) - (- 16 x^{2})}{10 x^{2} y^{2}}$

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

$\frac{- (35 y^{2} - 16 x^{2})}{10 x^{2} y^{2}}$

Simplify the expression.

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

$\frac{- 1 (35 y^{2} - 16 x^{2})}{10 x^{2} y^{2}}$

Move the negative in front of the fraction.

$- \frac{35 y^{2} - 16 x^{2}}{10 x^{2} y^{2}}$

Simplify (2x-7y)/(2x^2y)-(5y-8x)/(5xy^2)

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