Solve 3/y-y^2-9/y^3y/3+y

$$\frac{ 3 }{ y } - \frac{ { y }^{ 2 } -9 }{ { y }^{ 3 } } \frac{ y }{ 3+y }$$

Evaluate

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

Short Solution Steps

Multiply \frac{y^{2}-9}{y^{3}} times \frac{y}{3+y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{y}-\frac{\left(y^{2}-9\right)y}{y^{3}\left(3+y\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{3}{y}-\frac{y^{2}-9}{\left(y+3\right)y^{2}}$$

Factor the expressions that are not already factored in \frac{y^{2}-9}{\left(y+3\right)y^{2}}.

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

Cancel out y+3 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and y^{2} is y^{2}. Multiply \frac{3}{y} times \frac{y}{y}.

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

Since \frac{3y}{y^{2}} and \frac{y-3}{y^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3y-\left(y-3\right).

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

Combine like terms in 3y-y+3.

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

Expand

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

Short Solution Steps

Multiply \frac{y^{2}-9}{y^{3}} times \frac{y}{3+y} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{y}-\frac{\left(y^{2}-9\right)y}{y^{3}\left(3+y\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{3}{y}-\frac{y^{2}-9}{\left(y+3\right)y^{2}}$$

Factor the expressions that are not already factored in \frac{y^{2}-9}{\left(y+3\right)y^{2}}.

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

Cancel out y+3 in both numerator and denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and y^{2} is y^{2}. Multiply \frac{3}{y} times \frac{y}{y}.

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

Since \frac{3y}{y^{2}} and \frac{y-3}{y^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3y-\left(y-3\right).

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

Combine like terms in 3y-y+3.

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