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

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

Solve for x

$$x=-1$$

$$x=1$$

Steps Using Difference of Squares

Variable x cannot be equal to any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+2\right), the least common multiple of x,x+2.

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

Use the distributive property to multiply x by x+2.

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

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

$$2x^{2}+4x-\left(x+2\right)=x\times 3$$

To find the opposite of x+2, find the opposite of each term.

$$2x^{2}+4x-x-2=x\times 3$$

Combine 4x and -x to get 3x.

$$2x^{2}+3x-2=x\times 3$$

Subtract x\times 3 from both sides.

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

Combine 3x and -x\times 3 to get 0.

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

Divide both sides by 2.

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

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 any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+2\right), the least common multiple of x,x+2.

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

Use the distributive property to multiply x by x+2.

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

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

$$2x^{2}+4x-\left(x+2\right)=x\times 3$$

To find the opposite of x+2, find the opposite of each term.

$$2x^{2}+4x-x-2=x\times 3$$

Combine 4x and -x to get 3x.

$$2x^{2}+3x-2=x\times 3$$

Subtract x\times 3 from both sides.

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

Combine 3x and -x\times 3 to get 0.

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

Add 2 to both sides. Anything plus zero gives itself.

$$2x^{2}=2$$

Divide both sides by 2.

$$x^{2}=\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$x^{2}=1$$

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 any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by x\left(x+2\right), the least common multiple of x,x+2.

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

Use the distributive property to multiply x by x+2.

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

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

$$2x^{2}+4x-\left(x+2\right)=x\times 3$$

To find the opposite of x+2, find the opposite of each term.

$$2x^{2}+4x-x-2=x\times 3$$

Combine 4x and -x to get 3x.

$$2x^{2}+3x-2=x\times 3$$

Subtract x\times 3 from both sides.

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

Combine 3x and -x\times 3 to get 0.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-2\right)}}{2\times 2}$$

Multiply -8 times -2.

$$x=\frac{0±\sqrt{16}}{2\times 2}$$

Take the square root of 16.

$$x=\frac{0±4}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4}{4}$$

Now solve the equation x=\frac{0±4}{4} when ± is plus. Divide 4 by 4.

$$x=1$$

Now solve the equation x=\frac{0±4}{4} when ± is minus. Divide -4 by 4.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$