Solve 2x-3/2+x=2(x-3)/6+x

$$\frac { 2 x - 3 } { 2 + x } = \frac { 2 ( x - 3 ) } { 6 + x }$$

Solve for x

$$x=\frac{6}{11}\approx 0.545454545$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x+6 by 2x-3 and combine like terms.

$$2x^{2}+9x-18=\left(x+2\right)\times 2\left(x-3\right)$$

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

$$2x^{2}+9x-18=\left(2x+4\right)\left(x-3\right)$$

Use the distributive property to multiply 2x+4 by x-3 and combine like terms.

$$2x^{2}+9x-18=2x^{2}-2x-12$$

Subtract 2x^{2} from both sides.

$$2x^{2}+9x-18-2x^{2}=-2x-12$$

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

$$9x-18=-2x-12$$

Add 2x to both sides.

$$9x-18+2x=-12$$

Combine 9x and 2x to get 11x.

$$11x-18=-12$$

Add 18 to both sides.

$$11x=-12+18$$

Add -12 and 18 to get 6.

$$11x=6$$

Divide both sides by 11.

$$x=\frac{6}{11}$$