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

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

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

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

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

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

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$x^{2}+2x+1-x^{2}+2x-1=x-3$$

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

$$2x+1+2x-1=x-3$$

Combine 2x and 2x to get 4x.

$$4x+1-1=x-3$$

Subtract 1 from 1 to get 0.

$$4x=x-3$$

Subtract x from both sides.

$$4x-x=-3$$

Combine 4x and -x to get 3x.

$$3x=-3$$

Divide both sides by 3.

$$x=\frac{-3}{3}$$

Divide -3 by 3 to get -1.

$$x=-1$$