Solve x-2y/xleft(1+x-2y/yright)+1

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

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

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

$$\frac{x-2y}{x}\times \frac{y+x-2y}{y}+1$$

Combine like terms in y+x-2y.

$$\frac{x-2y}{x}\times \frac{-y+x}{y}+1$$

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

$$\frac{\left(x-2y\right)\left(-y+x\right)}{xy}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{xy}{xy}.

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

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

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

Do the multiplications in \left(x-2y\right)\left(-y+x\right)+xy.

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

Combine like terms in -xy+x^{2}+2y^{2}-2yx+xy.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.

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

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

$$\frac{x-2y}{x}\times \frac{y+x-2y}{y}+1$$

Combine like terms in y+x-2y.

$$\frac{x-2y}{x}\times \frac{-y+x}{y}+1$$

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

$$\frac{\left(x-2y\right)\left(-y+x\right)}{xy}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{xy}{xy}.

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

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

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

Do the multiplications in \left(x-2y\right)\left(-y+x\right)+xy.

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

Combine like terms in -xy+x^{2}+2y^{2}-2yx+xy.

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