Solve 6y+3/y:(4y^2-4/y^2:3y+3/4y+2)

$$\frac { 6 y + 3 } { y } : ( \frac { 4 y ^ { 2 } - 4 } { y ^ { 2 } } : \frac { 3 y + 3 } { 4 y + 2 } )$$

Evaluate

$$\frac{9y}{8\left(y-1\right)}$$

Short Solution Steps

Divide \frac{6y+3}{y} by \frac{\frac{4y^{2}-4}{y^{2}}}{\frac{3y+3}{4y+2}} by multiplying \frac{6y+3}{y} by the reciprocal of \frac{\frac{4y^{2}-4}{y^{2}}}{\frac{3y+3}{4y+2}}.

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

Express \left(6y+3\right)\times \frac{3y+3}{4y+2} as a single fraction.

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

Express y\times \frac{4y^{2}-4}{y^{2}} as a single fraction.

$$\frac{\frac{\left(6y+3\right)\left(3y+3\right)}{4y+2}}{\frac{y\left(4y^{2}-4\right)}{y^{2}}}$$

Cancel out y in both numerator and denominator.

$$\frac{\frac{\left(6y+3\right)\left(3y+3\right)}{4y+2}}{\frac{4y^{2}-4}{y}}$$

Divide \frac{\left(6y+3\right)\left(3y+3\right)}{4y+2} by \frac{4y^{2}-4}{y} by multiplying \frac{\left(6y+3\right)\left(3y+3\right)}{4y+2} by the reciprocal of \frac{4y^{2}-4}{y}.

$$\frac{\left(6y+3\right)\left(3y+3\right)y}{\left(4y+2\right)\left(4y^{2}-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(y+1\right)\left(2y+1\right) in both numerator and denominator.

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

Expand the expression.

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

Expand

$$\frac{9y}{8\left(y-1\right)}$$

Short Solution Steps

Divide \frac{6y+3}{y} by \frac{\frac{4y^{2}-4}{y^{2}}}{\frac{3y+3}{4y+2}} by multiplying \frac{6y+3}{y} by the reciprocal of \frac{\frac{4y^{2}-4}{y^{2}}}{\frac{3y+3}{4y+2}}.

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

Express \left(6y+3\right)\times \frac{3y+3}{4y+2} as a single fraction.

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

Express y\times \frac{4y^{2}-4}{y^{2}} as a single fraction.

$$\frac{\frac{\left(6y+3\right)\left(3y+3\right)}{4y+2}}{\frac{y\left(4y^{2}-4\right)}{y^{2}}}$$

Cancel out y in both numerator and denominator.

$$\frac{\frac{\left(6y+3\right)\left(3y+3\right)}{4y+2}}{\frac{4y^{2}-4}{y}}$$

Divide \frac{\left(6y+3\right)\left(3y+3\right)}{4y+2} by \frac{4y^{2}-4}{y} by multiplying \frac{\left(6y+3\right)\left(3y+3\right)}{4y+2} by the reciprocal of \frac{4y^{2}-4}{y}.

$$\frac{\left(6y+3\right)\left(3y+3\right)y}{\left(4y+2\right)\left(4y^{2}-4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(y+1\right)\left(2y+1\right) in both numerator and denominator.

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

Expand the expression.

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