Solve 5/x^2-x-20-3/x^2-25=3/x^2+9x+20

$$\frac { 5 } { x ^ { 2 } - x - 20 } - \frac { 3 } { x ^ { 2 } - 25 } = \frac { 3 } { x ^ { 2 } + 9 x + 20 }$$

Solve for x

$$x=28$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,-4,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+4\right)\left(x+5\right), the least common multiple of x^{2}-x-20,x^{2}-25,x^{2}+9x+20.

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

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

$$5x+25-\left(x+4\right)\times 3=\left(x-5\right)\times 3$$

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

$$5x+25-\left(3x+12\right)=\left(x-5\right)\times 3$$

To find the opposite of 3x+12, find the opposite of each term.

$$5x+25-3x-12=\left(x-5\right)\times 3$$

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

$$2x+25-12=\left(x-5\right)\times 3$$

Subtract 12 from 25 to get 13.

$$2x+13=\left(x-5\right)\times 3$$

Use the distributive property to multiply x-5 by 3.

$$2x+13=3x-15$$

Subtract 3x from both sides.

$$2x+13-3x=-15$$

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

$$-x+13=-15$$

Subtract 13 from both sides.

$$-x=-15-13$$

Subtract 13 from -15 to get -28.

$$-x=-28$$

Multiply both sides by -1.

$$x=28$$