Simplify (x+y)/(x^2y)-(x-2y)/(xy^2)

$\frac{x + y}{x^{2} y} - \frac{x - 2 y}{x y^{2}}$

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

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

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

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

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

Multiply $\frac{x + y}{x^{2} y}$ by $\frac{y}{y}$ .

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

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

$\frac{(x + y) y}{x^{2} (y^{1} y)} - \frac{x - 2 y}{x y^{2}} \cdot \frac{x}{x}$

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

$\frac{(x + y) y}{x^{2} (y^{1} y^{1})} - \frac{x - 2 y}{x y^{2}} \cdot \frac{x}{x}$

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

$\frac{(x + y) y}{x^{2} y^{1 + 1}} - \frac{x - 2 y}{x y^{2}} \cdot \frac{x}{x}$

Add $1$ and $1$ .

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

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

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

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

$\frac{(x + y) y}{x^{2} y^{2}} - \frac{(x - 2 y) x}{x^{1} x y^{2}}$

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

$\frac{(x + y) y}{x^{2} y^{2}} - \frac{(x - 2 y) x}{x^{1} x^{1} y^{2}}$

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

$\frac{(x + y) y}{x^{2} y^{2}} - \frac{(x - 2 y) x}{x^{1 + 1} y^{2}}$

Add $1$ and $1$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $y$ by $y$ .

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

Apply the distributive property.

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

Multiply $- 2$ by $- 1$ .

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

Apply the distributive property.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

$\frac{x y + y^{2} - x^{2} + 2 y x}{x^{2} y^{2}}$

Add $x y$ and $2 y x$ .

Move $y$ .

$\frac{y^{2} - x^{2} + x y + 2 x y}{x^{2} y^{2}}$

Add $x y$ and $2 x y$ .

$\frac{y^{2} - x^{2} + 3 x y}{x^{2} y^{2}}$

Simplify (x+y)/(x^2y)-(x-2y)/(xy^2)

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