Solve 4/x^2+2x-24+3/x^2+x-20=4/x^2+11x+30

$$\frac{ 4 }{ { x }^{ 2 } +2x-24 } + \frac{ 3 }{ { x }^{ 2 } +x-20 } = \frac{ 4 }{ { x }^{ 2 } +11x+30 }$$

Solve for x

$$x=-18$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,-5,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x+5\right)\left(x+6\right), the least common multiple of x^{2}+2x-24,x^{2}+x-20,x^{2}+11x+30.

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

Use the distributive property to multiply x+5 by 4.

$$4x+20+\left(x+6\right)\times 3=\left(x-4\right)\times 4$$

Use the distributive property to multiply x+6 by 3.

$$4x+20+3x+18=\left(x-4\right)\times 4$$

Combine 4x and 3x to get 7x.

$$7x+20+18=\left(x-4\right)\times 4$$

Add 20 and 18 to get 38.

$$7x+38=\left(x-4\right)\times 4$$

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

$$7x+38=4x-16$$

Subtract 4x from both sides.

$$7x+38-4x=-16$$

Combine 7x and -4x to get 3x.

$$3x+38=-16$$

Subtract 38 from both sides.

$$3x=-16-38$$

Subtract 38 from -16 to get -54.

$$3x=-54$$

Divide both sides by 3.

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

Divide -54 by 3 to get -18.

$$x=-18$$