Solve 9y^2-4/4y-12div9y^2+12y+1/18-6y

$$\frac { 9 y ^ { 2 } - 4 } { 4 y - 12 } \div \frac { 9 y ^ { 2 } + 12 y + 1 } { 18 - 6 y }$$

Evaluate

$$-\frac{3\left(9y^{2}-4\right)}{2\left(9y^{2}+12y+1\right)}$$

Short Solution Steps

Divide \frac{9y^{2}-4}{4y-12} by \frac{9y^{2}+12y+1}{18-6y} by multiplying \frac{9y^{2}-4}{4y-12} by the reciprocal of \frac{9y^{2}+12y+1}{18-6y}.

$$\frac{\left(9y^{2}-4\right)\left(18-6y\right)}{\left(4y-12\right)\left(9y^{2}+12y+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{6\left(3y-2\right)\left(-y+3\right)\left(3y+2\right)}{4\times 9\left(y-3\right)\left(y-\left(-\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)\left(y-\left(\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)}$$

Extract the negative sign in 3-y.

$$\frac{-6\left(y-3\right)\left(3y-2\right)\left(3y+2\right)}{4\times 9\left(y-3\right)\left(y-\left(-\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)\left(y-\left(\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)}$$

Cancel out 2\times 3\left(y-3\right) in both numerator and denominator.

$$\frac{-\left(3y-2\right)\left(3y+2\right)}{2\times 3\left(y-\left(-\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)\left(y-\left(\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)}$$

Expand the expression.

$$\frac{-9y^{2}+4}{6y^{2}+8y+\frac{2}{3}}$$

Expand

$$-\frac{3\left(9y^{2}-4\right)}{2\left(9y^{2}+12y+1\right)}$$

Short Solution Steps

Divide \frac{9y^{2}-4}{4y-12} by \frac{9y^{2}+12y+1}{18-6y} by multiplying \frac{9y^{2}-4}{4y-12} by the reciprocal of \frac{9y^{2}+12y+1}{18-6y}.

$$\frac{\left(9y^{2}-4\right)\left(18-6y\right)}{\left(4y-12\right)\left(9y^{2}+12y+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{6\left(3y-2\right)\left(-y+3\right)\left(3y+2\right)}{4\times 9\left(y-3\right)\left(y-\left(-\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)\left(y-\left(\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)}$$

Extract the negative sign in 3-y.

$$\frac{-6\left(y-3\right)\left(3y-2\right)\left(3y+2\right)}{4\times 9\left(y-3\right)\left(y-\left(-\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)\left(y-\left(\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)}$$

Cancel out 2\times 3\left(y-3\right) in both numerator and denominator.

$$\frac{-\left(3y-2\right)\left(3y+2\right)}{2\times 3\left(y-\left(-\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)\left(y-\left(\frac{1}{3}\sqrt{3}-\frac{2}{3}\right)\right)}$$

Expand the expression.

$$\frac{-9y^{2}+4}{6y^{2}+8y+\frac{2}{3}}$$