Solve left(x^2/y-y^2/yright)3/x+y

$$\left( \frac{ { x }^{ 2 } }{ y } - \frac{ { y }^{ 2 } }{ y } \right) \frac{ 3 }{ x+y }$$

Evaluate

$$\frac{3x}{y}-3$$

Short Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\left(\frac{x^{2}}{y}-y^{1}\right)\times \frac{3}{x+y}$$

Calculate y to the power of 1 and get y.

$$\left(\frac{x^{2}}{y}-y\right)\times \frac{3}{x+y}$$

Use the distributive property to multiply \frac{x^{2}}{y}-y by \frac{3}{x+y}.

$$\frac{x^{2}}{y}\times \frac{3}{x+y}+\left(-y\right)\times \frac{3}{x+y}$$

Multiply \frac{x^{2}}{y} times \frac{3}{x+y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}\times 3}{y\left(x+y\right)}+\left(-y\right)\times \frac{3}{x+y}$$

Express \left(-y\right)\times \frac{3}{x+y} as a single fraction.

$$\frac{x^{2}\times 3}{y\left(x+y\right)}+\frac{-y\times 3}{x+y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y\left(x+y\right) and x+y is y\left(x+y\right). Multiply \frac{-y\times 3}{x+y} times \frac{y}{y}.

$$\frac{x^{2}\times 3}{y\left(x+y\right)}+\frac{-y\times 3y}{y\left(x+y\right)}$$

Since \frac{x^{2}\times 3}{y\left(x+y\right)} and \frac{-y\times 3y}{y\left(x+y\right)} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}\times 3-y\times 3y}{y\left(x+y\right)}$$

Do the multiplications in x^{2}\times 3-y\times 3y.

$$\frac{x^{2}\times 3-3y^{2}}{y\left(x+y\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}\times 3-3y^{2}}{y\left(x+y\right)}.

$$\frac{3\left(x+y\right)\left(x-y\right)}{y\left(x+y\right)}$$

Cancel out x+y in both numerator and denominator.

$$\frac{3\left(x-y\right)}{y}$$

Use the distributive property to multiply 3 by x-y.

$$\frac{3x-3y}{y}$$

Expand

$$\frac{3x}{y}-3$$

Short Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\left(\frac{x^{2}}{y}-y^{1}\right)\times \frac{3}{x+y}$$

Calculate y to the power of 1 and get y.

$$\left(\frac{x^{2}}{y}-y\right)\times \frac{3}{x+y}$$

Use the distributive property to multiply \frac{x^{2}}{y}-y by \frac{3}{x+y}.

$$\frac{x^{2}}{y}\times \frac{3}{x+y}+\left(-y\right)\times \frac{3}{x+y}$$

Multiply \frac{x^{2}}{y} times \frac{3}{x+y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x^{2}\times 3}{y\left(x+y\right)}+\left(-y\right)\times \frac{3}{x+y}$$

Express \left(-y\right)\times \frac{3}{x+y} as a single fraction.

$$\frac{x^{2}\times 3}{y\left(x+y\right)}+\frac{-y\times 3}{x+y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y\left(x+y\right) and x+y is y\left(x+y\right). Multiply \frac{-y\times 3}{x+y} times \frac{y}{y}.

$$\frac{x^{2}\times 3}{y\left(x+y\right)}+\frac{-y\times 3y}{y\left(x+y\right)}$$

Since \frac{x^{2}\times 3}{y\left(x+y\right)} and \frac{-y\times 3y}{y\left(x+y\right)} have the same denominator, add them by adding their numerators.

$$\frac{x^{2}\times 3-y\times 3y}{y\left(x+y\right)}$$

Do the multiplications in x^{2}\times 3-y\times 3y.

$$\frac{x^{2}\times 3-3y^{2}}{y\left(x+y\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}\times 3-3y^{2}}{y\left(x+y\right)}.

$$\frac{3\left(x+y\right)\left(x-y\right)}{y\left(x+y\right)}$$

Cancel out x+y in both numerator and denominator.

$$\frac{3\left(x-y\right)}{y}$$

Use the distributive property to multiply 3 by x-y.

$$\frac{3x-3y}{y}$$