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

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

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

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 \left(x-1\right)\left(x+1\right), the least common multiple of x+1,x-1.

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

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

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

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

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

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

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

Subtract 2 from -3 to get -5.

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

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

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

Subtract 3x from both sides.

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

Combine 3x and -3x to get 0.

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

Add 5 to both sides.

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

Add 3 and 5 to get 8.

$$2x^{2}=8$$

Divide both sides by 2.

$$x^{2}=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

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 \left(x-1\right)\left(x+1\right), the least common multiple of x+1,x-1.

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

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

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

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

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

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

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

Subtract 2 from -3 to get -5.

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

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

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

Subtract 3x from both sides.

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

Combine 3x and -3x to get 0.

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

Subtract 3 from both sides.

$$-5+2x^{2}-3=0$$

Subtract 3 from -5 to get -8.

$$-8+2x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$2x^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-8\right)}}{2\times 2}$$

Multiply -4 times 2.

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

Multiply -8 times -8.

$$x=\frac{0±\sqrt{64}}{2\times 2}$$

Take the square root of 64.

$$x=\frac{0±8}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±8}{4}$$

Now solve the equation x=\frac{0±8}{4} when ± is plus. Divide 8 by 4.

$$x=2$$

Now solve the equation x=\frac{0±8}{4} when ± is minus. Divide -8 by 4.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$