Solve x-24/2x^2-9x-18=x/x-6-2x/2x+3

$$\frac { x - 24 } { 2 x ^ { 2 } - 9 x - 18 } = \frac { x } { x - 6 } - \frac { 2 x } { 2 x + 3 }$$

Solve for x

$$x = -\frac{12}{7} = -1\frac{5}{7} \approx -1.714285714$$

Steps for Solving Linear Equation

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

$$x-24=\left(2x+3\right)x-\left(x-6\right)\times 2x$$

Use the distributive property to multiply 2x+3 by x.

$$x-24=2x^{2}+3x-\left(x-6\right)\times 2x$$

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

$$x-24=2x^{2}+3x-\left(2x-12\right)x$$

Use the distributive property to multiply 2x-12 by x.

$$x-24=2x^{2}+3x-\left(2x^{2}-12x\right)$$

To find the opposite of 2x^{2}-12x, find the opposite of each term.

$$x-24=2x^{2}+3x-2x^{2}+12x$$

Combine 2x^{2} and -2x^{2} to get 0.

$$x-24=3x+12x$$

Combine 3x and 12x to get 15x.

$$x-24=15x$$

Subtract 15x from both sides.

$$x-24-15x=0$$

Combine x and -15x to get -14x.

$$-14x-24=0$$

Add 24 to both sides. Anything plus zero gives itself.

$$-14x=24$$

Divide both sides by -14.

$$x=\frac{24}{-14}$$

Reduce the fraction \frac{24}{-14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{12}{7}$$