Solve =1/y^2-1/1+frac{1{y}}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y^{2}}{y^{2}}.

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

Since \frac{1}{y^{2}} and \frac{y^{2}}{y^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{y}{y} and \frac{1}{y} have the same denominator, add them by adding their numerators.

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

Divide \frac{1-y^{2}}{y^{2}} by \frac{y+1}{y} by multiplying \frac{1-y^{2}}{y^{2}} by the reciprocal of \frac{y+1}{y}.

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

Cancel out y in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1-y.

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

Cancel out y+1 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y^{2}}{y^{2}}.

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

Since \frac{1}{y^{2}} and \frac{y^{2}}{y^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{y}{y} and \frac{1}{y} have the same denominator, add them by adding their numerators.

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

Divide \frac{1-y^{2}}{y^{2}} by \frac{y+1}{y} by multiplying \frac{1-y^{2}}{y^{2}} by the reciprocal of \frac{y+1}{y}.

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

Cancel out y in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1-y.

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

Cancel out y+1 in both numerator and denominator.

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

Expand the expression.

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