Solve 4/x^2+9x+18-1/x+3=1/3x+18

$$\frac { 4 } { x ^ { 2 } + 9 x + 18 } - \frac { 1 } { x + 3 } = \frac { 1 } { 3 x + 18 }$$

Solve for x

$$x = -\frac{9}{4} = -2\frac{1}{4} = -2.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,-3 since division by zero is not defined. Multiply both sides of the equation by 3\left(x+3\right)\left(x+6\right), the least common multiple of x^{2}+9x+18,x+3,3x+18.

$$3\times 4-\left(3x+18\right)=x+3$$

Multiply 3 and 4 to get 12.

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

To find the opposite of 3x+18, find the opposite of each term.

$$12-3x-18=x+3$$

Subtract 18 from 12 to get -6.

$$-6-3x=x+3$$

Subtract x from both sides.

$$-6-3x-x=3$$

Combine -3x and -x to get -4x.

$$-6-4x=3$$

Add 6 to both sides.

$$-4x=3+6$$

Add 3 and 6 to get 9.

$$-4x=9$$

Divide both sides by -4.

$$x=\frac{9}{-4}$$

Fraction \frac{9}{-4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$x=-\frac{9}{4}$$