Solve 3/x+5-6/x-4=12/x^2+x-20

$$\frac { 3 } { x + 5 } - \frac { 6 } { x - 4 } = \frac { 12 } { x ^ { 2 } + x - 20 }$$

Solve for x

$$x=-18$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+5\right), the least common multiple of x+5,x-4,x^{2}+x-20.

$$\left(x-4\right)\times 3-\left(x+5\right)\times 6=12$$

Use the distributive property to multiply x-4 by 3.

$$3x-12-\left(x+5\right)\times 6=12$$

Use the distributive property to multiply x+5 by 6.

$$3x-12-\left(6x+30\right)=12$$

To find the opposite of 6x+30, find the opposite of each term.

$$3x-12-6x-30=12$$

Combine 3x and -6x to get -3x.

$$-3x-12-30=12$$

Subtract 30 from -12 to get -42.

$$-3x-42=12$$

Add 42 to both sides.

$$-3x=12+42$$

Add 12 and 42 to get 54.

$$-3x=54$$

Divide both sides by -3.

$$x=\frac{54}{-3}$$

Divide 54 by -3 to get -18.

$$x=-18$$