Solve 2x-2/4x-1=x-1/2x+2

$$\frac { 2 x - 2 } { 4 x - 1 } = \frac { x - 1 } { 2 x + 2 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,\frac{1}{4} since division by zero is not defined. Multiply both sides of the equation by 2\left(4x-1\right)\left(x+1\right), the least common multiple of 4x-1,2x+2.

$$\left(2x+2\right)\left(2x-2\right)=\left(4x-1\right)\left(x-1\right)$$

Consider \left(2x+2\right)\left(2x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$\left(2x\right)^{2}-4=\left(4x-1\right)\left(x-1\right)$$

Expand \left(2x\right)^{2}.

$$2^{2}x^{2}-4=\left(4x-1\right)\left(x-1\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-4=\left(4x-1\right)\left(x-1\right)$$

Use the distributive property to multiply 4x-1 by x-1 and combine like terms.

$$4x^{2}-4=4x^{2}-5x+1$$

Subtract 4x^{2} from both sides.

$$4x^{2}-4-4x^{2}=-5x+1$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-4=-5x+1$$

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

$$-5x+1=-4$$

Subtract 1 from both sides.

$$-5x=-4-1$$

Subtract 1 from -4 to get -5.

$$-5x=-5$$

Divide both sides by -5.

$$x=\frac{-5}{-5}$$

Divide -5 by -5 to get 1.

$$x=1$$