Solve (x+2xy+y^2/x)divx+y/x

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

Evaluate

$$x+y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{\frac{xx}{x}+\frac{2xy+y^{2}}{x}}{\frac{x+y}{x}}$$

Since \frac{xx}{x} and \frac{2xy+y^{2}}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{xx+2xy+y^{2}}{x}}{\frac{x+y}{x}}$$

Do the multiplications in xx+2xy+y^{2}.

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

Divide \frac{x^{2}+2xy+y^{2}}{x} by \frac{x+y}{x} by multiplying \frac{x^{2}+2xy+y^{2}}{x} by the reciprocal of \frac{x+y}{x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

$$x+y$$

Expand

$$x+y$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{\frac{xx}{x}+\frac{2xy+y^{2}}{x}}{\frac{x+y}{x}}$$

Since \frac{xx}{x} and \frac{2xy+y^{2}}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{xx+2xy+y^{2}}{x}}{\frac{x+y}{x}}$$

Do the multiplications in xx+2xy+y^{2}.

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

Divide \frac{x^{2}+2xy+y^{2}}{x} by \frac{x+y}{x} by multiplying \frac{x^{2}+2xy+y^{2}}{x} by the reciprocal of \frac{x+y}{x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+y in both numerator and denominator.

$$x+y$$