Solve 1/3x+12-2=5/x+4

$$\frac{ 1 }{ 3x+12 } -2= \frac{ 5 }{ x+4 }$$

Solve for x

$$x = -\frac{19}{3} = -6\frac{1}{3} \approx -6.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+4\right), the least common multiple of 3x+12,x+4.

$$1+3\left(x+4\right)\left(-2\right)=3\times 5$$

Multiply 3 and -2 to get -6.

$$1-6\left(x+4\right)=3\times 5$$

Use the distributive property to multiply -6 by x+4.

$$1-6x-24=3\times 5$$

Subtract 24 from 1 to get -23.

$$-23-6x=3\times 5$$

Multiply 3 and 5 to get 15.

$$-23-6x=15$$

Add 23 to both sides.

$$-6x=15+23$$

Add 15 and 23 to get 38.

$$-6x=38$$

Divide both sides by -6.

$$x=\frac{38}{-6}$$

Reduce the fraction \frac{38}{-6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{19}{3}$$