Solve 8x/x^2-3x-4=4/x+1-8/x-4

$$\frac { 8 x } { x ^ { 2 } - 3 x - 4 } = \frac { 4 } { x + 1 } - \frac { 8 } { x - 4 }$$

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 \left(x-4\right)\left(x+1\right), the least common multiple of x^{2}-3x-4,x+1,x-4.

$$8x=\left(x-4\right)\times 4-\left(x+1\right)\times 8$$

Use the distributive property to multiply x-4 by 4.

$$8x=4x-16-\left(x+1\right)\times 8$$

Use the distributive property to multiply x+1 by 8.

$$8x=4x-16-\left(8x+8\right)$$

To find the opposite of 8x+8, find the opposite of each term.

$$8x=4x-16-8x-8$$

Combine 4x and -8x to get -4x.

$$8x=-4x-16-8$$

Subtract 8 from -16 to get -24.

$$8x=-4x-24$$

Add 4x to both sides.

$$8x+4x=-24$$

Combine 8x and 4x to get 12x.

$$12x=-24$$

Divide both sides by 12.

$$x=\frac{-24}{12}$$

Divide -24 by 12 to get -2.

$$x=-2$$