Solve y=1/2+1/t-1

$$y = \frac { 1 } { 2 } + \frac { 1 } { t - 1 }$$

Solve for t

$$t=-\frac{2y+1}{1-2y}$$

$$y\neq \frac{1}{2}$$

Steps for Solving Linear Equation

Variable t cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(t-1\right), the least common multiple of 2,t-1.

$$y\times 2\left(t-1\right)=2\left(t-1\right)\times \frac{1}{2}+2$$

Use the distributive property to multiply y\times 2 by t-1.

$$2yt-y\times 2=2\left(t-1\right)\times \frac{1}{2}+2$$

Multiply -1 and 2 to get -2.

$$2yt-2y=2\left(t-1\right)\times \frac{1}{2}+2$$

Multiply 2 and \frac{1}{2} to get 1.

$$2yt-2y=t-1+2$$

Add -1 and 2 to get 1.

$$2yt-2y=t+1$$

Subtract t from both sides.

$$2yt-2y-t=1$$

Add 2y to both sides.

$$2yt-t=1+2y$$

Combine all terms containing t.

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

The equation is in standard form.

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

Divide both sides by 2y-1.

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

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

$$t=\frac{2y+1}{2y-1}$$

Variable t cannot be equal to 1.

$$t=\frac{2y+1}{2y-1}\text{, }t\neq 1$$

Solve for y

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

$$t\neq 1$$