Solve y+4/y^2+16y+48*y^2-144/y-8=?

$$\frac { y + 4 } { y ^ { 2 } + 16 y + 48 } \times \frac { y ^ { 2 } - 144 } { y - 8 } = ?$$

Evaluate

$$\frac{y-12}{y-8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y+4}{y^{2}+16y+48}.

$$\frac{y+4}{\left(y+4\right)\left(y+12\right)}\times \frac{y^{2}-144}{y-8}$$

Cancel out y+4 in both numerator and denominator.

$$\frac{1}{y+12}\times \frac{y^{2}-144}{y-8}$$

Multiply \frac{1}{y+12} times \frac{y^{2}-144}{y-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y^{2}-144}{\left(y+12\right)\left(y-8\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-12\right)\left(y+12\right)}{\left(y-8\right)\left(y+12\right)}$$

Cancel out y+12 in both numerator and denominator.

$$\frac{y-12}{y-8}$$

Expand

$$\frac{y-12}{y-8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y+4}{y^{2}+16y+48}.

$$\frac{y+4}{\left(y+4\right)\left(y+12\right)}\times \frac{y^{2}-144}{y-8}$$

Cancel out y+4 in both numerator and denominator.

$$\frac{1}{y+12}\times \frac{y^{2}-144}{y-8}$$

Multiply \frac{1}{y+12} times \frac{y^{2}-144}{y-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{y^{2}-144}{\left(y+12\right)\left(y-8\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-12\right)\left(y+12\right)}{\left(y-8\right)\left(y+12\right)}$$

Cancel out y+12 in both numerator and denominator.

$$\frac{y-12}{y-8}$$