Solve left(2+xright)left(x+1right)=left(3+2xright)left(x-1right)-1*(x-1)(x+1)

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2+x by x+1 and combine like terms.

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

Use the distributive property to multiply 3+2x by x-1 and combine like terms.

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

Add 1\left(x-1\right)\left(x+1\right) to both sides.

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

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

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

Consider \left(x-1\right)\left(x+1\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 1.

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

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

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

Subtract 1 from 2 to get 1.

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

Subtract x from both sides.

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

Combine 3x and -x to get 2x.

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

Subtract 2x^{2} from both sides.

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

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

$$2x+1=-3$$

Subtract 1 from both sides.

$$2x=-3-1$$

Subtract 1 from -3 to get -4.

$$2x=-4$$

Divide both sides by 2.

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

Divide -4 by 2 to get -2.

$$x=-2$$