Solve y^2-9/y^2*y^2-3y/y^2+7y-30

$$\frac { y ^ { 2 } - 9 } { y ^ { 2 } } \cdot \frac { y ^ { 2 } - 3 y } { y ^ { 2 } + 7 y - 30 }$$

Evaluate

$$\frac{y^{2}-9}{y\left(y+10\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-3y}{y^{2}+7y-30}.

$$\frac{y^{2}-9}{y^{2}}\times \frac{y\left(y-3\right)}{\left(y-3\right)\left(y+10\right)}$$

Cancel out y-3 in both numerator and denominator.

$$\frac{y^{2}-9}{y^{2}}\times \frac{y}{y+10}$$

Multiply \frac{y^{2}-9}{y^{2}} times \frac{y}{y+10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-9\right)y}{y^{2}\left(y+10\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y^{2}-9}{y\left(y+10\right)}$$

Use the distributive property to multiply y by y+10.

$$\frac{y^{2}-9}{y^{2}+10y}$$

Expand

$$\frac{y^{2}-9}{y\left(y+10\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-3y}{y^{2}+7y-30}.

$$\frac{y^{2}-9}{y^{2}}\times \frac{y\left(y-3\right)}{\left(y-3\right)\left(y+10\right)}$$

Cancel out y-3 in both numerator and denominator.

$$\frac{y^{2}-9}{y^{2}}\times \frac{y}{y+10}$$

Multiply \frac{y^{2}-9}{y^{2}} times \frac{y}{y+10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-9\right)y}{y^{2}\left(y+10\right)}$$

Cancel out y in both numerator and denominator.

$$\frac{y^{2}-9}{y\left(y+10\right)}$$

Use the distributive property to multiply y by y+10.

$$\frac{y^{2}-9}{y^{2}+10y}$$