Solve x/1-frac{1{x}}-y

$$\frac { x } { 1 - \frac { 1 } { x } } - y$$

Evaluate

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

Short Solution Steps

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

$$\frac{x}{\frac{x}{x}-\frac{1}{x}}-y$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{\frac{x-1}{x}}-y$$

Divide x by \frac{x-1}{x} by multiplying x by the reciprocal of \frac{x-1}{x}.

$$\frac{xx}{x-1}-y$$

Multiply x and x to get x^{2}.

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

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

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

Since \frac{x^{2}}{x-1} and \frac{y\left(x-1\right)}{x-1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-y\left(x-1\right).

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

Differentiate w.r.t. x

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