Solve frac{12y^{3}+8y^2}{9y^2-4}div24y^3/9y^2-12y+4

$$\frac { 12 y ^ { 3 } + 8 y ^ { 2 } } { 9 y ^ { 2 } - 4 } \div \frac { 24 y ^ { 3 } } { 9 y ^ { 2 } - 12 y + 4 }$$

Evaluate

$$\frac{1}{2}-\frac{1}{3y}$$

Short Solution Steps

Divide \frac{12y^{3}+8y^{2}}{9y^{2}-4} by \frac{24y^{3}}{9y^{2}-12y+4} by multiplying \frac{12y^{3}+8y^{2}}{9y^{2}-4} by the reciprocal of \frac{24y^{3}}{9y^{2}-12y+4}.

$$\frac{\left(12y^{3}+8y^{2}\right)\left(9y^{2}-12y+4\right)}{\left(9y^{2}-4\right)\times 24y^{3}}$$

Factor the expressions that are not already factored.

$$\frac{4\left(3y+2\right)y^{2}\left(3y-2\right)^{2}}{24\left(3y-2\right)\left(3y+2\right)y^{3}}$$

Cancel out 4\left(3y-2\right)\left(3y+2\right)y^{2} in both numerator and denominator.

$$\frac{3y-2}{6y}$$

Expand

$$\frac{1}{2}-\frac{1}{3y}$$

Short Solution Steps

Divide \frac{12y^{3}+8y^{2}}{9y^{2}-4} by \frac{24y^{3}}{9y^{2}-12y+4} by multiplying \frac{12y^{3}+8y^{2}}{9y^{2}-4} by the reciprocal of \frac{24y^{3}}{9y^{2}-12y+4}.

$$\frac{\left(12y^{3}+8y^{2}\right)\left(9y^{2}-12y+4\right)}{\left(9y^{2}-4\right)\times 24y^{3}}$$

Factor the expressions that are not already factored.

$$\frac{4\left(3y+2\right)y^{2}\left(3y-2\right)^{2}}{24\left(3y-2\right)\left(3y+2\right)y^{3}}$$

Cancel out 4\left(3y-2\right)\left(3y+2\right)y^{2} in both numerator and denominator.

$$\frac{3y-2}{6y}$$