Solve 9/x+2=2x/x+3

$$\frac { 9 } { x } + 2 = \frac { 2 x } { x + 3 }$$

Solve for x

$$x = -\frac{9}{5} = -1\frac{4}{5} = -1.8$$

Steps for Solving Linear Equation

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

$$\left(x+3\right)\times 9+x\left(x+3\right)\times 2=x\times 2x$$

Use the distributive property to multiply x+3 by 9.

$$9x+27+x\left(x+3\right)\times 2=x\times 2x$$

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

$$9x+27+\left(x^{2}+3x\right)\times 2=x\times 2x$$

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

$$9x+27+2x^{2}+6x=x\times 2x$$

Combine 9x and 6x to get 15x.

$$15x+27+2x^{2}=x\times 2x$$

Multiply x and x to get x^{2}.

$$15x+27+2x^{2}=x^{2}\times 2$$

Subtract x^{2}\times 2 from both sides.

$$15x+27+2x^{2}-x^{2}\times 2=0$$

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

$$15x+27=0$$

Subtract 27 from both sides. Anything subtracted from zero gives its negation.

$$15x=-27$$

Divide both sides by 15.

$$x=\frac{-27}{15}$$

Reduce the fraction \frac{-27}{15} to lowest terms by extracting and canceling out 3.

$$x=-\frac{9}{5}$$