Solve 1/x-5+9/x+9=10/x^2+4x-45

$$\frac { 1 } { x - 5 } + \frac { 9 } { x + 9 } = \frac { 10 } { x ^ { 2 } + 4 x - 45 }$$

Solve for x

$$x = \frac{23}{5} = 4\frac{3}{5} = 4.6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -9,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+9\right), the least common multiple of x-5,x+9,x^{2}+4x-45.

$$x+9+\left(x-5\right)\times 9=10$$

Use the distributive property to multiply x-5 by 9.

$$x+9+9x-45=10$$

Combine x and 9x to get 10x.

$$10x+9-45=10$$

Subtract 45 from 9 to get -36.

$$10x-36=10$$

Add 36 to both sides.

$$10x=10+36$$

Add 10 and 36 to get 46.

$$10x=46$$

Divide both sides by 10.

$$x=\frac{46}{10}$$

Reduce the fraction \frac{46}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{23}{5}$$