Solve x+1/3-x+1/x+2=0

$$\frac { x + 1 } { 3 } - \frac { x + 1 } { x + 2 } = 0$$

Solve for x

$$x=1$$

$$x=-1$$

Steps Using Difference of Squares

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+2\right), the least common multiple of 3,x+2.

$$\left(x+2\right)\left(x+1\right)-3\left(x+1\right)=0$$

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

$$x^{2}+3x+2-3\left(x+1\right)=0$$

Use the distributive property to multiply -3 by x+1.

$$x^{2}+3x+2-3x-3=0$$

Combine 3x and -3x to get 0.

$$x^{2}+2-3=0$$

Subtract 3 from 2 to get -1.

$$x^{2}-1=0$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

To find equation solutions, solve x-1=0 and x+1=0.

$$x=1 x=-1$$

Steps by Finding Square Root

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+2\right), the least common multiple of 3,x+2.

$$\left(x+2\right)\left(x+1\right)-3\left(x+1\right)=0$$

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

$$x^{2}+3x+2-3\left(x+1\right)=0$$

Use the distributive property to multiply -3 by x+1.

$$x^{2}+3x+2-3x-3=0$$

Combine 3x and -3x to get 0.

$$x^{2}+2-3=0$$

Subtract 3 from 2 to get -1.

$$x^{2}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+2\right), the least common multiple of 3,x+2.

$$\left(x+2\right)\left(x+1\right)-3\left(x+1\right)=0$$

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

$$x^{2}+3x+2-3\left(x+1\right)=0$$

Use the distributive property to multiply -3 by x+1.

$$x^{2}+3x+2-3x-3=0$$

Combine 3x and -3x to get 0.

$$x^{2}+2-3=0$$

Subtract 3 from 2 to get -1.

$$x^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)}}{2}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4}}{2}$$

Take the square root of 4.

$$x=\frac{0±2}{2}$$

Now solve the equation x=\frac{0±2}{2} when ± is plus. Divide 2 by 2.

$$x=1$$

Now solve the equation x=\frac{0±2}{2} when ± is minus. Divide -2 by 2.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$