Solve y^2-2y-63/y^2-14y+49divy-9/y-7

$$\frac { y ^ { 2 } - 2 y - 63 } { y ^ { 2 } - 14 y + 49 } \div \frac { y - 9 } { y - 7 }$$

Evaluate

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

Short Solution Steps

Divide \frac{y^{2}-2y-63}{y^{2}-14y+49} by \frac{y-9}{y-7} by multiplying \frac{y^{2}-2y-63}{y^{2}-14y+49} by the reciprocal of \frac{y-9}{y-7}.

$$\frac{\left(y^{2}-2y-63\right)\left(y-7\right)}{\left(y^{2}-14y+49\right)\left(y-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-9\right)\left(y-7\right)\left(y+7\right)}{\left(y-9\right)\left(y-7\right)^{2}}$$

Cancel out \left(y-9\right)\left(y-7\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{y^{2}-2y-63}{y^{2}-14y+49} by \frac{y-9}{y-7} by multiplying \frac{y^{2}-2y-63}{y^{2}-14y+49} by the reciprocal of \frac{y-9}{y-7}.

$$\frac{\left(y^{2}-2y-63\right)\left(y-7\right)}{\left(y^{2}-14y+49\right)\left(y-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-9\right)\left(y-7\right)\left(y+7\right)}{\left(y-9\right)\left(y-7\right)^{2}}$$

Cancel out \left(y-9\right)\left(y-7\right) in both numerator and denominator.

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