Solve (1/(x-1)^2-3/2x-2=-3/2x+2)

$$( \frac { 1 } { ( x - 1 ) ^ { 2 } } - \frac { 3 } { 2 x - 2 } = \frac { - 3 } { 2 x + 2 } )$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

$$2x+2-\left(x^{2}-1\right)\times 3=\left(x-1\right)^{2}\left(-3\right)$$

Use the distributive property to multiply x^{2}-1 by 3.

$$2x+2-\left(3x^{2}-3\right)=\left(x-1\right)^{2}\left(-3\right)$$

To find the opposite of 3x^{2}-3, find the opposite of each term.

$$2x+2-3x^{2}+3=\left(x-1\right)^{2}\left(-3\right)$$

Add 2 and 3 to get 5.

$$2x+5-3x^{2}=\left(x-1\right)^{2}\left(-3\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$2x+5-3x^{2}=\left(x^{2}-2x+1\right)\left(-3\right)$$

Use the distributive property to multiply x^{2}-2x+1 by -3.

$$2x+5-3x^{2}=-3x^{2}+6x-3$$

Add 3x^{2} to both sides.

$$2x+5-3x^{2}+3x^{2}=6x-3$$

Combine -3x^{2} and 3x^{2} to get 0.

$$2x+5=6x-3$$

Subtract 6x from both sides.

$$2x+5-6x=-3$$

Combine 2x and -6x to get -4x.

$$-4x+5=-3$$

Subtract 5 from both sides.

$$-4x=-3-5$$

Subtract 5 from -3 to get -8.

$$-4x=-8$$

Divide both sides by -4.

$$x=\frac{-8}{-4}$$

Divide -8 by -4 to get 2.

$$x=2$$