Solve 13/x-2/9x=3/x+9

$$\frac { 13 } { x } - \frac { 2 } { 9 x } = \frac { 3 } { x + 9 }$$

Solve for x

$$x = -\frac{1035}{88} = -11\frac{67}{88} \approx -11.761363636$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -9,0 since division by zero is not defined. Multiply both sides of the equation by 9x\left(x+9\right), the least common multiple of x,9x,x+9.

$$\left(9x+81\right)\times 13-\left(x+9\right)\times 2=9x\times 3$$

Use the distributive property to multiply 9x+81 by 13.

$$117x+1053-\left(x+9\right)\times 2=9x\times 3$$

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

$$117x+1053-\left(2x+18\right)=9x\times 3$$

To find the opposite of 2x+18, find the opposite of each term.

$$117x+1053-2x-18=9x\times 3$$

Combine 117x and -2x to get 115x.

$$115x+1053-18=9x\times 3$$

Subtract 18 from 1053 to get 1035.

$$115x+1035=9x\times 3$$

Multiply 9 and 3 to get 27.

$$115x+1035=27x$$

Subtract 27x from both sides.

$$115x+1035-27x=0$$

Combine 115x and -27x to get 88x.

$$88x+1035=0$$

Subtract 1035 from both sides. Anything subtracted from zero gives its negation.

$$88x=-1035$$

Divide both sides by 88.

$$x=\frac{-1035}{88}$$

Fraction \frac{-1035}{88} can be rewritten as -\frac{1035}{88} by extracting the negative sign.

$$x=-\frac{1035}{88}$$