Solve y^2+8y-80/2y^2-2y-112divy^2-64/y^2-49

$$\frac { y ^ { 2 } + 8 y - 80 } { 2 y ^ { 2 } - 2 y - 112 } \div \frac { y ^ { 2 } - 64 } { y ^ { 2 } - 49 }$$

Evaluate

$$\frac{\left(y-7\right)\left(y^{2}+8y-80\right)}{2\left(y+8\right)\left(y-8\right)^{2}}$$

Short Solution Steps

Divide \frac{y^{2}+8y-80}{2y^{2}-2y-112} by \frac{y^{2}-64}{y^{2}-49} by multiplying \frac{y^{2}+8y-80}{2y^{2}-2y-112} by the reciprocal of \frac{y^{2}-64}{y^{2}-49}.

$$\frac{\left(y^{2}+8y-80\right)\left(y^{2}-49\right)}{\left(2y^{2}-2y-112\right)\left(y^{2}-64\right)}$$

Factor the expressions that are not already factored.

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

Cancel out y+7 in both numerator and denominator.

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

Expand the expression.

$$\frac{y^{3}+y^{2}-136y+560}{2y^{3}-16y^{2}-128y+1024}$$

Expand

$$\frac{y^{3}+y^{2}-136y+560}{2\left(y-8\right)\left(y^{2}-64\right)}$$

Short Solution Steps

Divide \frac{y^{2}+8y-80}{2y^{2}-2y-112} by \frac{y^{2}-64}{y^{2}-49} by multiplying \frac{y^{2}+8y-80}{2y^{2}-2y-112} by the reciprocal of \frac{y^{2}-64}{y^{2}-49}.

$$\frac{\left(y^{2}+8y-80\right)\left(y^{2}-49\right)}{\left(2y^{2}-2y-112\right)\left(y^{2}-64\right)}$$

Factor the expressions that are not already factored.

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

Cancel out y+7 in both numerator and denominator.

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

Expand the expression.

$$\frac{y^{3}+y^{2}-136y+560}{2y^{3}-16y^{2}-128y+1024}$$