Solve 18y^2-74y+8/9y^2+80y-9/frac{36y^2-13y+1{4y^2+35y-9}}

$$\frac { \frac { 18 y ^ { 2 } - 74 y + 8 } { 9 y ^ { 2 } + 80 y - 9 } } { \frac { 36 y ^ { 2 } - 13 y + 1 } { 4 y ^ { 2 } + 35 y - 9 } }$$

Evaluate

$$\frac{2\left(y-4\right)}{9y-1}$$

Short Solution Steps

Divide \frac{18y^{2}-74y+8}{9y^{2}+80y-9} by \frac{36y^{2}-13y+1}{4y^{2}+35y-9} by multiplying \frac{18y^{2}-74y+8}{9y^{2}+80y-9} by the reciprocal of \frac{36y^{2}-13y+1}{4y^{2}+35y-9}.

$$\frac{\left(18y^{2}-74y+8\right)\left(4y^{2}+35y-9\right)}{\left(9y^{2}+80y-9\right)\left(36y^{2}-13y+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(y-4\right)\left(4y-1\right)\left(9y-1\right)\left(y+9\right)}{\left(4y-1\right)\left(y+9\right)\left(9y-1\right)^{2}}$$

Cancel out \left(4y-1\right)\left(9y-1\right)\left(y+9\right) in both numerator and denominator.

$$\frac{2\left(y-4\right)}{9y-1}$$

Expand the expression.

$$\frac{2y-8}{9y-1}$$

Expand

$$\frac{2\left(y-4\right)}{9y-1}$$

Short Solution Steps

Divide \frac{18y^{2}-74y+8}{9y^{2}+80y-9} by \frac{36y^{2}-13y+1}{4y^{2}+35y-9} by multiplying \frac{18y^{2}-74y+8}{9y^{2}+80y-9} by the reciprocal of \frac{36y^{2}-13y+1}{4y^{2}+35y-9}.

$$\frac{\left(18y^{2}-74y+8\right)\left(4y^{2}+35y-9\right)}{\left(9y^{2}+80y-9\right)\left(36y^{2}-13y+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(y-4\right)\left(4y-1\right)\left(9y-1\right)\left(y+9\right)}{\left(4y-1\right)\left(y+9\right)\left(9y-1\right)^{2}}$$

Cancel out \left(4y-1\right)\left(9y-1\right)\left(y+9\right) in both numerator and denominator.

$$\frac{2\left(y-4\right)}{9y-1}$$

Expand the expression.

$$\frac{2y-8}{9y-1}$$