Solve 1-2y/x+y^2/x^2/x-y

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{x}{x} and \frac{2y}{x} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-2y}{x} times \frac{x}{x}.

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

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

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

Do the multiplications in \left(x-2y\right)x+y^{2}.

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

Express \frac{\frac{x^{2}-2yx+y^{2}}{x^{2}}}{x-y} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

Since \frac{x}{x} and \frac{2y}{x} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-2y}{x} times \frac{x}{x}.

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

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

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

Do the multiplications in \left(x-2y\right)x+y^{2}.

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

Express \frac{\frac{x^{2}-2yx+y^{2}}{x^{2}}}{x-y} as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

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