Solve 3/2x+8-1/x-3=3/x+4

$$\frac { 3 } { 2 x + 8 } - \frac { 1 } { x - 3 } = \frac { 3 } { x + 4 }$$

Solve for x

$$x=\frac{1}{5}=0.2$$

Steps for Solving Linear Equation

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

$$\left(x-3\right)\times 3-\left(2x+8\right)=\left(2x-6\right)\times 3$$

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

$$3x-9-\left(2x+8\right)=\left(2x-6\right)\times 3$$

To find the opposite of 2x+8, find the opposite of each term.

$$3x-9-2x-8=\left(2x-6\right)\times 3$$

Combine 3x and -2x to get x.

$$x-9-8=\left(2x-6\right)\times 3$$

Subtract 8 from -9 to get -17.

$$x-17=\left(2x-6\right)\times 3$$

Use the distributive property to multiply 2x-6 by 3.

$$x-17=6x-18$$

Subtract 6x from both sides.

$$x-17-6x=-18$$

Combine x and -6x to get -5x.

$$-5x-17=-18$$

Add 17 to both sides.

$$-5x=-18+17$$

Add -18 and 17 to get -1.

$$-5x=-1$$

Divide both sides by -5.

$$x=\frac{-1}{-5}$$

Fraction \frac{-1}{-5} can be simplified to \frac{1}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{5}$$