Solve y=2(2ydiv(9y-2))/9(2ydiv(9y-2))-2

$$y= \frac{ 2(2y \div (9y-2)) }{ 9(2y \div (9y-2))-2 }$$

Solve for y

$$y\neq \frac{2}{9}$$

Short Solution Steps

Express 2\times \frac{2y}{9y-2} as a single fraction.

$$y=\frac{\frac{2\times 2y}{9y-2}}{9\times \frac{2y}{9y-2}-2}$$

Express 9\times \frac{2y}{9y-2} as a single fraction.

$$y=\frac{\frac{2\times 2y}{9y-2}}{\frac{9\times 2y}{9y-2}-2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{9y-2}{9y-2}.

$$y=\frac{\frac{2\times 2y}{9y-2}}{\frac{9\times 2y}{9y-2}-\frac{2\left(9y-2\right)}{9y-2}}$$

Since \frac{9\times 2y}{9y-2} and \frac{2\left(9y-2\right)}{9y-2} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{\frac{2\times 2y}{9y-2}}{\frac{9\times 2y-2\left(9y-2\right)}{9y-2}}$$

Do the multiplications in 9\times 2y-2\left(9y-2\right).

$$y=\frac{\frac{2\times 2y}{9y-2}}{\frac{18y-18y+4}{9y-2}}$$

Combine like terms in 18y-18y+4.

$$y=\frac{\frac{2\times 2y}{9y-2}}{\frac{4}{9y-2}}$$

Variable y cannot be equal to \frac{2}{9} since division by zero is not defined. Divide \frac{2\times 2y}{9y-2} by \frac{4}{9y-2} by multiplying \frac{2\times 2y}{9y-2} by the reciprocal of \frac{4}{9y-2}.

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

Cancel out 2\times 2 in both numerator and denominator.

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

Use the distributive property to multiply y by 9y-2.

$$y=\frac{9y^{2}-2y}{9y-2}$$

Subtract \frac{9y^{2}-2y}{9y-2} from both sides.

$$y-\frac{9y^{2}-2y}{9y-2}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{9y-2}{9y-2}.

$$\frac{y\left(9y-2\right)}{9y-2}-\frac{9y^{2}-2y}{9y-2}=0$$

Since \frac{y\left(9y-2\right)}{9y-2} and \frac{9y^{2}-2y}{9y-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y\left(9y-2\right)-\left(9y^{2}-2y\right)}{9y-2}=0$$

Do the multiplications in y\left(9y-2\right)-\left(9y^{2}-2y\right).

$$\frac{9y^{2}-2y-9y^{2}+2y}{9y-2}=0$$

Combine like terms in 9y^{2}-2y-9y^{2}+2y.

$$\frac{0}{9y-2}=0$$

Variable y cannot be equal to \frac{2}{9} since division by zero is not defined. Multiply both sides of the equation by 9y-2.

$$0=0$$

This is true for any y.

$$y\in \mathrm{R}$$

Variable y cannot be equal to \frac{2}{9}.

$$y\in \mathrm{R}\setminus \frac{2}{9}$$