Solve 3x/x+2=3/2x

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

Solve for x

$$x=0$$

Steps by Finding Square Root

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

$$2\times 3x=\frac{3}{2}x\times 2\left(x+2\right)$$

Multiply 2 and 3 to get 6.

$$6x=\frac{3}{2}x\times 2\left(x+2\right)$$

Multiply \frac{3}{2} and 2 to get 3.

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

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

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

Subtract 3x^{2} from both sides.

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

Subtract 6x from both sides.

$$6x-3x^{2}-6x=0$$

Combine 6x and -6x to get 0.

$$-3x^{2}=0$$

Divide both sides by -3. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

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

$$2\times 3x=\frac{3}{2}x\times 2\left(x+2\right)$$

Multiply 2 and 3 to get 6.

$$6x=\frac{3}{2}x\times 2\left(x+2\right)$$

Multiply \frac{3}{2} and 2 to get 3.

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

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

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

Subtract 3x^{2} from both sides.

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

Subtract 6x from both sides.

$$6x-3x^{2}-6x=0$$

Combine 6x and -6x to get 0.

$$-3x^{2}=0$$

Divide both sides by -3. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$