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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and y is y^{2}. Multiply \frac{y-1}{y} times \frac{y}{y}.

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

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

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

Do the multiplications in 1-\left(y-1\right)y.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and y-2 is \left(y-2\right)y^{2}. Multiply \frac{1-y^{2}+y}{y^{2}} times \frac{y-2}{y-2}. Multiply \frac{y}{y-2} times \frac{y^{2}}{y^{2}}.

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

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

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

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

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

Combine like terms in y-2-y^{3}+2y^{2}+y^{2}-2y+y^{3}.

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

Expand \left(y-2\right)y^{2}.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and y is y^{2}. Multiply \frac{y-1}{y} times \frac{y}{y}.

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

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

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

Do the multiplications in 1-\left(y-1\right)y.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y^{2} and y-2 is \left(y-2\right)y^{2}. Multiply \frac{1-y^{2}+y}{y^{2}} times \frac{y-2}{y-2}. Multiply \frac{y}{y-2} times \frac{y^{2}}{y^{2}}.

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

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

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

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

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

Combine like terms in y-2-y^{3}+2y^{2}+y^{2}-2y+y^{3}.

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

Expand \left(y-2\right)y^{2}.

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