Solve 15/x+9x-7/x+2=9

$$\frac { 15 } { x } + \frac { 9 x - 7 } { x + 2 } = 9$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

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

$$\left(x+2\right)\times 15+x\left(9x-7\right)=9x\left(x+2\right)$$

Use the distributive property to multiply x+2 by 15.

$$15x+30+x\left(9x-7\right)=9x\left(x+2\right)$$

Use the distributive property to multiply x by 9x-7.

$$15x+30+9x^{2}-7x=9x\left(x+2\right)$$

Combine 15x and -7x to get 8x.

$$8x+30+9x^{2}=9x\left(x+2\right)$$

Use the distributive property to multiply 9x by x+2.

$$8x+30+9x^{2}=9x^{2}+18x$$

Subtract 9x^{2} from both sides.

$$8x+30+9x^{2}-9x^{2}=18x$$

Combine 9x^{2} and -9x^{2} to get 0.

$$8x+30=18x$$

Subtract 18x from both sides.

$$8x+30-18x=0$$

Combine 8x and -18x to get -10x.

$$-10x+30=0$$

Subtract 30 from both sides. Anything subtracted from zero gives its negation.

$$-10x=-30$$

Divide both sides by -10.

$$x=\frac{-30}{-10}$$

Divide -30 by -10 to get 3.

$$x=3$$