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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,4 since division by zero is not defined. Multiply both sides of the equation by 2\left(x-4\right)\left(x+1\right), the least common multiple of x^{2}-3x-4,x-4,2x+2.

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

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

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

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

$$2x+4=6x+6-\left(x-4\right)$$

To find the opposite of x-4, find the opposite of each term.

$$2x+4=6x+6-x+4$$

Combine 6x and -x to get 5x.

$$2x+4=5x+6+4$$

Add 6 and 4 to get 10.

$$2x+4=5x+10$$

Subtract 5x from both sides.

$$2x+4-5x=10$$

Combine 2x and -5x to get -3x.

$$-3x+4=10$$

Subtract 4 from both sides.

$$-3x=10-4$$

Subtract 4 from 10 to get 6.

$$-3x=6$$

Divide both sides by -3.

$$x=\frac{6}{-3}$$

Divide 6 by -3 to get -2.

$$x=-2$$