Solve 4/x^2+3x-10+1/x^2+9x+20=2/x^2+2x-8

$$\frac { 4 } { x ^ { 2 } + 3 x - 10 } + \frac { 1 } { x ^ { 2 } + 9 x + 20 } = \frac { 2 } { x ^ { 2 } + 2 x - 8 }$$

Solve for x

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,-4,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+4\right)\left(x+5\right), the least common multiple of x^{2}+3x-10,x^{2}+9x+20,x^{2}+2x-8.

$$\left(x+4\right)\times 4+x-2=\left(x+5\right)\times 2$$

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

$$4x+16+x-2=\left(x+5\right)\times 2$$

Combine 4x and x to get 5x.

$$5x+16-2=\left(x+5\right)\times 2$$

Subtract 2 from 16 to get 14.

$$5x+14=\left(x+5\right)\times 2$$

Use the distributive property to multiply x+5 by 2.

$$5x+14=2x+10$$

Subtract 2x from both sides.

$$5x+14-2x=10$$

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

$$3x+14=10$$

Subtract 14 from both sides.

$$3x=10-14$$

Subtract 14 from 10 to get -4.

$$3x=-4$$

Divide both sides by 3.

$$x=\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$x=-\frac{4}{3}$$