Solve 1-3(x+2)/x=4/x^2-2x-2/x-2

$$1 - \frac { 3 ( x + 2 ) } { x } = \frac { 4 } { x ^ { 2 } - 2 x } - \frac { 2 } { x - 2 }$$

Solve for x

$$x=-2$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values 0,2 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}-2x,x-2.

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

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

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

Use the distributive property to multiply x-2 by 3.

$$x^{2}-2x-\left(3x-6\right)\left(x+2\right)=4-x\times 2$$

Use the distributive property to multiply 3x-6 by x+2 and combine like terms.

$$x^{2}-2x-\left(3x^{2}-12\right)=4-x\times 2$$

To find the opposite of 3x^{2}-12, find the opposite of each term.

$$x^{2}-2x-3x^{2}+12=4-x\times 2$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

$$-2x^{2}-2x+12=4-x\times 2$$

Add x\times 2 to both sides.

$$-2x^{2}-2x+12+x\times 2=4$$

Combine -2x and x\times 2 to get 0.

$$-2x^{2}+12=4$$

Subtract 12 from both sides.

$$-2x^{2}=4-12$$

Subtract 12 from 4 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.

$$x=2 x=-2$$

Variable x cannot be equal to 2.

$$x=-2$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values 0,2 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}-2x,x-2.

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

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

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

Use the distributive property to multiply x-2 by 3.

$$x^{2}-2x-\left(3x-6\right)\left(x+2\right)=4-x\times 2$$

Use the distributive property to multiply 3x-6 by x+2 and combine like terms.

$$x^{2}-2x-\left(3x^{2}-12\right)=4-x\times 2$$

To find the opposite of 3x^{2}-12, find the opposite of each term.

$$x^{2}-2x-3x^{2}+12=4-x\times 2$$

Combine x^{2} and -3x^{2} to get -2x^{2}.

$$-2x^{2}-2x+12=4-x\times 2$$

Subtract 4 from both sides.

$$-2x^{2}-2x+12-4=-x\times 2$$

Subtract 4 from 12 to get 8.

$$-2x^{2}-2x+8=-x\times 2$$

Add x\times 2 to both sides.

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

Combine -2x and x\times 2 to get 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}.

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

Square 0.

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

Multiply -4 times -2.

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

Multiply 8 times 8.

$$x=\frac{0±\sqrt{64}}{2\left(-2\right)}$$

Take the square root of 64.

$$x=\frac{0±8}{2\left(-2\right)}$$

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.

$$x=-2 x=2$$

Variable x cannot be equal to 2.

$$x=-2$$