Solve 3x-1/x^2+7x+12=1/2x+6+7/6x+24

$$\frac { 3 x - 1 } { x ^ { 2 } + 7 x + 12 } = \frac { 1 } { 2 x + 6 } + \frac { 7 } { 6 x + 24 }$$

Solve for x

$$x = \frac{39}{8} = 4\frac{7}{8} = 4.875$$

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 6\left(x+3\right)\left(x+4\right), the least common multiple of x^{2}+7x+12,2x+6,6x+24.

$$6\left(3x-1\right)=3x+12+\left(x+3\right)\times 7$$

Use the distributive property to multiply 6 by 3x-1.

$$18x-6=3x+12+\left(x+3\right)\times 7$$

Use the distributive property to multiply x+3 by 7.

$$18x-6=3x+12+7x+21$$

Combine 3x and 7x to get 10x.

$$18x-6=10x+12+21$$

Add 12 and 21 to get 33.

$$18x-6=10x+33$$

Subtract 10x from both sides.

$$18x-6-10x=33$$

Combine 18x and -10x to get 8x.

$$8x-6=33$$

Add 6 to both sides.

$$8x=33+6$$

Add 33 and 6 to get 39.

$$8x=39$$

Divide both sides by 8.

$$x=\frac{39}{8}$$