Solve s/3x+2-3/2x-3=4

$$\frac { s } { 3 x + 2 } - \frac { 3 } { 2 x - 3 } = 4$$

Solve for s

$$s=-\frac{\left(9-8x\right)\left(3x+2\right)}{2x-3}$$

$$x\neq -\frac{2}{3}\text{ and }x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(2x-3\right)\left(3x+2\right), the least common multiple of 3x+2,2x-3.

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

Use the distributive property to multiply 2x-3 by s.

$$2xs-3s-\left(3x+2\right)\times 3=4\left(2x-3\right)\left(3x+2\right)$$

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

$$2xs-3s-\left(9x+6\right)=4\left(2x-3\right)\left(3x+2\right)$$

To find the opposite of 9x+6, find the opposite of each term.

$$2xs-3s-9x-6=4\left(2x-3\right)\left(3x+2\right)$$

Use the distributive property to multiply 4 by 2x-3.

$$2xs-3s-9x-6=\left(8x-12\right)\left(3x+2\right)$$

Use the distributive property to multiply 8x-12 by 3x+2 and combine like terms.

$$2xs-3s-9x-6=24x^{2}-20x-24$$

Add 9x to both sides.

$$2xs-3s-6=24x^{2}-20x-24+9x$$

Combine -20x and 9x to get -11x.

$$2xs-3s-6=24x^{2}-11x-24$$

Add 6 to both sides.

$$2xs-3s=24x^{2}-11x-24+6$$

Add -24 and 6 to get -18.

$$2xs-3s=24x^{2}-11x-18$$

Combine all terms containing s.

$$\left(2x-3\right)s=24x^{2}-11x-18$$

Divide both sides by 2x-3.

$$\frac{\left(2x-3\right)s}{2x-3}=\frac{\left(8x-9\right)\left(3x+2\right)}{2x-3}$$

Dividing by 2x-3 undoes the multiplication by 2x-3.

$$s=\frac{\left(8x-9\right)\left(3x+2\right)}{2x-3}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{\sqrt{4s^{2}-244s+1849}}{48}+\frac{s}{24}+\frac{11}{48}\text{, }&\text{unconditionally}\\x=-\frac{\sqrt{4s^{2}-244s+1849}}{48}+\frac{s}{24}+\frac{11}{48}\text{, }&s\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{4s^{2}-244s+1849}}{48}+\frac{s}{24}+\frac{11}{48}\text{, }&s\geq 6\sqrt{13}+\frac{61}{2}\text{ or }s\leq \frac{61}{2}-6\sqrt{13}\\x=-\frac{\sqrt{4s^{2}-244s+1849}}{48}+\frac{s}{24}+\frac{11}{48}\text{, }&s\geq 6\sqrt{13}+\frac{61}{2}\text{ or }\left(s\neq 0\text{ and }s\leq \frac{61}{2}-6\sqrt{13}\right)\end{matrix}\right.$$