Solve 5/2x-3/2x-6-1/x+2=0

$$\frac { 5 } { 2 x } - \frac { 3 } { 2 x - 6 } - \frac { 1 } { x + 2 } = 0$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,0,3 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x-3\right)\left(x+2\right), the least common multiple of 2x,2x-6,x+2.

$$\left(x-3\right)\left(x+2\right)\times 5-x\left(x+2\right)\times 3-2x\left(x-3\right)=0$$

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

$$\left(x^{2}-x-6\right)\times 5-x\left(x+2\right)\times 3-2x\left(x-3\right)=0$$

Use the distributive property to multiply x^{2}-x-6 by 5.

$$5x^{2}-5x-30-x\left(x+2\right)\times 3-2x\left(x-3\right)=0$$

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

$$5x^{2}-5x-30-\left(x^{2}+2x\right)\times 3-2x\left(x-3\right)=0$$

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

$$5x^{2}-5x-30-\left(3x^{2}+6x\right)-2x\left(x-3\right)=0$$

To find the opposite of 3x^{2}+6x, find the opposite of each term.

$$5x^{2}-5x-30-3x^{2}-6x-2x\left(x-3\right)=0$$

Combine 5x^{2} and -3x^{2} to get 2x^{2}.

$$2x^{2}-5x-30-6x-2x\left(x-3\right)=0$$

Combine -5x and -6x to get -11x.

$$2x^{2}-11x-30-2x\left(x-3\right)=0$$

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

$$2x^{2}-11x-30-2x^{2}+6x=0$$

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

$$-11x-30+6x=0$$

Combine -11x and 6x to get -5x.

$$-5x-30=0$$

Add 30 to both sides. Anything plus zero gives itself.

$$-5x=30$$

Divide both sides by -5.

$$x=\frac{30}{-5}$$

Divide 30 by -5 to get -6.

$$x=-6$$