Solve y=m/m-1(x-2m^2-1)+2m

$$y = \frac { m } { m - 1 } ( x - 2 m ^ { 2 } - 1 ) + 2 m$$

Solve for x

$$\left\{\begin{matrix}x=2m^{2}+y-2m-\frac{y}{m}+3\text{, }&m\neq 0\text{ and }m\neq 1\\x\in \mathrm{R}\text{, }&m=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by m-1.

$$y\left(m-1\right)=m\left(x-2m^{2}-1\right)+2m\left(m-1\right)$$

Use the distributive property to multiply y by m-1.

$$ym-y=m\left(x-2m^{2}-1\right)+2m\left(m-1\right)$$

Use the distributive property to multiply m by x-2m^{2}-1.

$$ym-y=mx-2m^{3}-m+2m\left(m-1\right)$$

Use the distributive property to multiply 2m by m-1.

$$ym-y=mx-2m^{3}-m+2m^{2}-2m$$

Combine -m and -2m to get -3m.

$$ym-y=mx-2m^{3}-3m+2m^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$mx-2m^{3}-3m+2m^{2}=ym-y$$

Add 2m^{3} to both sides.

$$mx-3m+2m^{2}=ym-y+2m^{3}$$

Add 3m to both sides.

$$mx+2m^{2}=ym-y+2m^{3}+3m$$

Subtract 2m^{2} from both sides.

$$mx=ym-y+2m^{3}+3m-2m^{2}$$

The equation is in standard form.

$$mx=my-y+2m^{3}-2m^{2}+3m$$

Divide both sides by m.

$$\frac{mx}{m}=\frac{my-y+2m^{3}-2m^{2}+3m}{m}$$

Dividing by m undoes the multiplication by m.

$$x=\frac{my-y+2m^{3}-2m^{2}+3m}{m}$$

Divide ym-y+2m^{3}+3m-2m^{2} by m.

$$x=2m^{2}+y-2m-\frac{y}{m}+3$$