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

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

Evaluate

$$\frac{y\left(y^{3}-1\right)}{y^{3}+y^{2}+1}$$

Short Solution Steps

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

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

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

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

Do the multiplications in y^{2}y-1.

$$\frac{\frac{y^{3}-1}{y}}{1+y+\frac{1}{y^{2}}}$$

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

$$\frac{\frac{y^{3}-1}{y}}{\frac{\left(1+y\right)y^{2}}{y^{2}}+\frac{1}{y^{2}}}$$

Since \frac{\left(1+y\right)y^{2}}{y^{2}} and \frac{1}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{3}-1}{y}}{\frac{\left(1+y\right)y^{2}+1}{y^{2}}}$$

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

$$\frac{\frac{y^{3}-1}{y}}{\frac{y^{2}+y^{3}+1}{y^{2}}}$$

Divide \frac{y^{3}-1}{y} by \frac{y^{2}+y^{3}+1}{y^{2}} by multiplying \frac{y^{3}-1}{y} by the reciprocal of \frac{y^{2}+y^{3}+1}{y^{2}}.

$$\frac{\left(y^{3}-1\right)y^{2}}{y\left(y^{2}+y^{3}+1\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y\left(y^{3}-1\right)}{y^{3}+y^{2}+1}$$

Use the distributive property to multiply y by y^{3}-1.

$$\frac{y^{4}-y}{y^{3}+y^{2}+1}$$

Expand

$$\frac{y^{4}-y}{y^{3}+y^{2}+1}$$

Short Solution Steps

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

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

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

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

Do the multiplications in y^{2}y-1.

$$\frac{\frac{y^{3}-1}{y}}{1+y+\frac{1}{y^{2}}}$$

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

$$\frac{\frac{y^{3}-1}{y}}{\frac{\left(1+y\right)y^{2}}{y^{2}}+\frac{1}{y^{2}}}$$

Since \frac{\left(1+y\right)y^{2}}{y^{2}} and \frac{1}{y^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{y^{3}-1}{y}}{\frac{\left(1+y\right)y^{2}+1}{y^{2}}}$$

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

$$\frac{\frac{y^{3}-1}{y}}{\frac{y^{2}+y^{3}+1}{y^{2}}}$$

Divide \frac{y^{3}-1}{y} by \frac{y^{2}+y^{3}+1}{y^{2}} by multiplying \frac{y^{3}-1}{y} by the reciprocal of \frac{y^{2}+y^{3}+1}{y^{2}}.

$$\frac{\left(y^{3}-1\right)y^{2}}{y\left(y^{2}+y^{3}+1\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y\left(y^{3}-1\right)}{y^{3}+y^{2}+1}$$

Use the distributive property to multiply y by y^{3}-1.

$$\frac{y^{4}-y}{y^{3}+y^{2}+1}$$