Solve g(y)=y^2-y-12/9y^3-5y^2*81y^3-25y/4y-16

$$g ( y ) = \frac { y ^ { 2 } - y - 12 } { 9 y ^ { 3 } - 5 y ^ { 2 } } \cdot \frac { 81 y ^ { 3 } - 25 y } { 4 y - 16 }$$

Evaluate

$$\frac{9y}{4}+8+\frac{15}{4y}$$

Short Solution Steps

Multiply \frac{y^{2}-y-12}{9y^{3}-5y^{2}} times \frac{81y^{3}-25y}{4y-16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-y-12\right)\left(81y^{3}-25y\right)}{\left(9y^{3}-5y^{2}\right)\left(4y-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{y\left(y-4\right)\left(9y-5\right)\left(y+3\right)\left(9y+5\right)}{4\left(y-4\right)\left(9y-5\right)y^{2}}$$

Cancel out y\left(y-4\right)\left(9y-5\right) in both numerator and denominator.

$$\frac{\left(y+3\right)\left(9y+5\right)}{4y}$$

Expand the expression.

$$\frac{9y^{2}+32y+15}{4y}$$

Expand

$$\frac{9y}{4}+8+\frac{15}{4y}$$

Short Solution Steps

Multiply \frac{y^{2}-y-12}{9y^{3}-5y^{2}} times \frac{81y^{3}-25y}{4y-16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y^{2}-y-12\right)\left(81y^{3}-25y\right)}{\left(9y^{3}-5y^{2}\right)\left(4y-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{y\left(y-4\right)\left(9y-5\right)\left(y+3\right)\left(9y+5\right)}{4\left(y-4\right)\left(9y-5\right)y^{2}}$$

Cancel out y\left(y-4\right)\left(9y-5\right) in both numerator and denominator.

$$\frac{\left(y+3\right)\left(9y+5\right)}{4y}$$

Expand the expression.

$$\frac{9y^{2}+32y+15}{4y}$$