Solve y^2-49/y^2+3y-28*y^2+6y+8/y^2-5y-14

$$\frac { y ^ { 2 } - 49 } { y ^ { 2 } + 3 y - 28 } \cdot \frac { y ^ { 2 } + 6 y + 8 } { y ^ { 2 } - 5 y - 14 }$$

Evaluate

$$\frac{y+4}{y-4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-49}{y^{2}+3y-28}.

$$\frac{\left(y-7\right)\left(y+7\right)}{\left(y-4\right)\left(y+7\right)}\times \frac{y^{2}+6y+8}{y^{2}-5y-14}$$

Cancel out y+7 in both numerator and denominator.

$$\frac{y-7}{y-4}\times \frac{y^{2}+6y+8}{y^{2}-5y-14}$$

Factor the expressions that are not already factored in \frac{y^{2}+6y+8}{y^{2}-5y-14}.

$$\frac{y-7}{y-4}\times \frac{\left(y+2\right)\left(y+4\right)}{\left(y-7\right)\left(y+2\right)}$$

Cancel out y+2 in both numerator and denominator.

$$\frac{y-7}{y-4}\times \frac{y+4}{y-7}$$

Multiply \frac{y-7}{y-4} times \frac{y+4}{y-7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y-7\right)\left(y+4\right)}{\left(y-4\right)\left(y-7\right)}$$

Cancel out y-7 in both numerator and denominator.

$$\frac{y+4}{y-4}$$

Expand

$$\frac{y+4}{y-4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}-49}{y^{2}+3y-28}.

$$\frac{\left(y-7\right)\left(y+7\right)}{\left(y-4\right)\left(y+7\right)}\times \frac{y^{2}+6y+8}{y^{2}-5y-14}$$

Cancel out y+7 in both numerator and denominator.

$$\frac{y-7}{y-4}\times \frac{y^{2}+6y+8}{y^{2}-5y-14}$$

Factor the expressions that are not already factored in \frac{y^{2}+6y+8}{y^{2}-5y-14}.

$$\frac{y-7}{y-4}\times \frac{\left(y+2\right)\left(y+4\right)}{\left(y-7\right)\left(y+2\right)}$$

Cancel out y+2 in both numerator and denominator.

$$\frac{y-7}{y-4}\times \frac{y+4}{y-7}$$

Multiply \frac{y-7}{y-4} times \frac{y+4}{y-7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y-7\right)\left(y+4\right)}{\left(y-4\right)\left(y-7\right)}$$

Cancel out y-7 in both numerator and denominator.

$$\frac{y+4}{y-4}$$