Solve y=(4t-1)(3t-2)^-1

$$y = ( 4 t - 1 ) ( 3 t - 2 ) ^ { - 1 }$$

Solve for t

$$t=-\frac{1-2y}{3y-4}$$

$$y\neq \frac{4}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4t-1 by \left(3t-2\right)^{-1}.

$$y=4t\left(3t-2\right)^{-1}-\left(3t-2\right)^{-1}$$

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

$$4t\left(3t-2\right)^{-1}-\left(3t-2\right)^{-1}=y$$

Reorder the terms.

$$4\times \frac{1}{3t-2}t-\frac{1}{3t-2}=y$$

Variable t cannot be equal to \frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by 3t-2.

$$4\times 1t-1=y\left(3t-2\right)$$

Do the multiplications.

$$4t-1=y\left(3t-2\right)$$

Use the distributive property to multiply y by 3t-2.

$$4t-1=3yt-2y$$

Subtract 3yt from both sides.

$$4t-1-3yt=-2y$$

Add 1 to both sides.

$$4t-3yt=-2y+1$$

Combine all terms containing t.

$$\left(4-3y\right)t=-2y+1$$

The equation is in standard form.

$$\left(4-3y\right)t=1-2y$$

Divide both sides by 4-3y.

$$\frac{\left(4-3y\right)t}{4-3y}=\frac{1-2y}{4-3y}$$

Dividing by 4-3y undoes the multiplication by 4-3y.

$$t=\frac{1-2y}{4-3y}$$

Variable t cannot be equal to \frac{2}{3}.

$$t=\frac{1-2y}{4-3y}\text{, }t\neq \frac{2}{3}$$

Solve for y

$$y=-\frac{1-4t}{3t-2}$$

$$t\neq \frac{2}{3}$$