Solve t/g=2x-1/x+2

$$t / g = \frac { 2 x - 1 } { x + 2 }$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{t\left(x+2\right)}{1-2x}\text{, }&x\neq -2\text{ and }t\neq 0\text{ and }x\neq \frac{1}{2}\\g\neq 0\text{, }&t=0\text{ and }x=\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by g\left(x+2\right), the least common multiple of g,x+2.

$$\left(x+2\right)t=g\left(2x-1\right)$$

Use the distributive property to multiply x+2 by t.

$$xt+2t=g\left(2x-1\right)$$

Use the distributive property to multiply g by 2x-1.

$$xt+2t=2gx-g$$

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

$$2gx-g=xt+2t$$

Combine all terms containing g.

$$\left(2x-1\right)g=xt+2t$$

The equation is in standard form.

$$\left(2x-1\right)g=tx+2t$$

Divide both sides by 2x-1.

$$\frac{\left(2x-1\right)g}{2x-1}=\frac{t\left(x+2\right)}{2x-1}$$

Dividing by 2x-1 undoes the multiplication by 2x-1.

$$g=\frac{t\left(x+2\right)}{2x-1}$$

Variable g cannot be equal to 0.

$$g=\frac{t\left(x+2\right)}{2x-1}\text{, }g\neq 0$$

Solve for t

$$t=-\frac{g\left(1-2x\right)}{x+2}$$

$$g\neq 0\text{ and }x\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by g\left(x+2\right), the least common multiple of g,x+2.

$$\left(x+2\right)t=g\left(2x-1\right)$$

Use the distributive property to multiply x+2 by t.

$$xt+2t=g\left(2x-1\right)$$

Use the distributive property to multiply g by 2x-1.

$$xt+2t=2gx-g$$

Combine all terms containing t.

$$\left(x+2\right)t=2gx-g$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)t}{x+2}=\frac{g\left(2x-1\right)}{x+2}$$

Dividing by x+2 undoes the multiplication by x+2.

$$t=\frac{g\left(2x-1\right)}{x+2}$$