Solve 3/x+2+1/3=2/x+2+3/2

$$\frac{ 3 }{ x+2 } + \frac{ 1 }{ 3 } = \frac{ 2 }{ x+2 } + \frac{ 3 }{ 2 }$$

Solve for x

$$x = -\frac{8}{7} = -1\frac{1}{7} \approx -1.142857143$$

Steps for Solving Linear Equation

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 6\left(x+2\right), the least common multiple of x+2,3,2.

$$6\times 3+6\left(x+2\right)\times \frac{1}{3}=6\times 2+6\left(x+2\right)\times \frac{3}{2}$$

Multiply 6 and 3 to get 18.

$$18+6\left(x+2\right)\times \frac{1}{3}=6\times 2+6\left(x+2\right)\times \frac{3}{2}$$

Multiply 6 and \frac{1}{3} to get 2.

$$18+2\left(x+2\right)=6\times 2+6\left(x+2\right)\times \frac{3}{2}$$

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

$$18+2x+4=6\times 2+6\left(x+2\right)\times \frac{3}{2}$$

Add 18 and 4 to get 22.

$$22+2x=6\times 2+6\left(x+2\right)\times \frac{3}{2}$$

Multiply 6 and 2 to get 12.

$$22+2x=12+6\left(x+2\right)\times \frac{3}{2}$$

Multiply 6 and \frac{3}{2} to get 9.

$$22+2x=12+9\left(x+2\right)$$

Use the distributive property to multiply 9 by x+2.

$$22+2x=12+9x+18$$

Add 12 and 18 to get 30.

$$22+2x=30+9x$$

Subtract 9x from both sides.

$$22+2x-9x=30$$

Combine 2x and -9x to get -7x.

$$22-7x=30$$

Subtract 22 from both sides.

$$-7x=30-22$$

Subtract 22 from 30 to get 8.

$$-7x=8$$

Divide both sides by -7.

$$x=\frac{8}{-7}$$

Fraction \frac{8}{-7} can be rewritten as -\frac{8}{7} by extracting the negative sign.

$$x=-\frac{8}{7}$$