Solve x/x-1=3a/2x-2-27

$$\frac { x } { x - 1 } = \frac { 3 a } { 2 x - 2 } - 27$$

Solve for a

$$a=\frac{56x}{3}-18$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-1\right), the least common multiple of x-1,2x-2.

$$2x=3a+2\left(x-1\right)\left(-27\right)$$

Multiply 2 and -27 to get -54.

$$2x=3a-54\left(x-1\right)$$

Use the distributive property to multiply -54 by x-1.

$$2x=3a-54x+54$$

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

$$3a-54x+54=2x$$

Add 54x to both sides.

$$3a+54=2x+54x$$

Combine 2x and 54x to get 56x.

$$3a+54=56x$$

Subtract 54 from both sides.

$$3a=56x-54$$

Divide both sides by 3.

$$\frac{3a}{3}=\frac{56x-54}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$a=\frac{56x-54}{3}$$

Divide 56x-54 by 3.

$$a=\frac{56x}{3}-18$$

Solve for x

$$x=\frac{3\left(a+18\right)}{56}$$

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

Steps for Solving Linear Equation

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

$$2x=3a+2\left(x-1\right)\left(-27\right)$$

Multiply 2 and -27 to get -54.

$$2x=3a-54\left(x-1\right)$$

Use the distributive property to multiply -54 by x-1.

$$2x=3a-54x+54$$

Add 54x to both sides.

$$2x+54x=3a+54$$

Combine 2x and 54x to get 56x.

$$56x=3a+54$$

Divide both sides by 56.

$$\frac{56x}{56}=\frac{3a+54}{56}$$

Dividing by 56 undoes the multiplication by 56.

$$x=\frac{3a+54}{56}$$

Divide 54+3a by 56.

$$x=\frac{3a}{56}+\frac{27}{28}$$

Variable x cannot be equal to 1.

$$x=\frac{3a}{56}+\frac{27}{28}\text{, }x\neq 1$$