Solve 2/x-3+2x/2x+3=1

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

Solve for x

$$x=-15$$

Steps for Solving Linear Equation

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

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

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

$$4x+6+\left(x-3\right)\times 2x=\left(x-3\right)\left(2x+3\right)$$

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

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

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

$$4x+6+2x^{2}-6x=\left(x-3\right)\left(2x+3\right)$$

Combine 4x and -6x to get -2x.

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

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

$$-2x+6+2x^{2}=2x^{2}-3x-9$$

Subtract 2x^{2} from both sides.

$$-2x+6+2x^{2}-2x^{2}=-3x-9$$

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

$$-2x+6=-3x-9$$

Add 3x to both sides.

$$-2x+6+3x=-9$$

Combine -2x and 3x to get x.

$$x+6=-9$$

Subtract 6 from both sides.

$$x=-9-6$$

Subtract 6 from -9 to get -15.

$$x=-15$$