Solve 25*1/x+3+4/x-3=8/x^2-9

$$25 \cdot \frac { 1 } { x + 3 } + \frac { 4 } { x - 3 } = \frac { 8 } { x ^ { 2 } - 9 }$$

Solve for x

$$x = \frac{71}{29} = 2\frac{13}{29} \approx 2.448275862$$

Steps for Solving Linear Equation

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

$$25\left(x-3\right)\times 1+\left(x+3\right)\times 4=8$$

Multiply 25 and 1 to get 25.

$$25\left(x-3\right)+\left(x+3\right)\times 4=8$$

Use the distributive property to multiply 25 by x-3.

$$25x-75+\left(x+3\right)\times 4=8$$

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

$$25x-75+4x+12=8$$

Combine 25x and 4x to get 29x.

$$29x-75+12=8$$

Add -75 and 12 to get -63.

$$29x-63=8$$

Add 63 to both sides.

$$29x=8+63$$

Add 8 and 63 to get 71.

$$29x=71$$

Divide both sides by 29.

$$x=\frac{71}{29}$$