Solve 17/x-3/8x=8/x+9

$$\frac { 17 } { x } - \frac { 3 } { 8 x } = \frac { 8 } { x + 9 }$$

Solve for x

$$x = -\frac{399}{23} = -17\frac{8}{23} \approx -17.347826087$$

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 8x\left(x+9\right), the least common multiple of x,8x,x+9.

$$\left(8x+72\right)\times 17-\left(x+9\right)\times 3=8x\times 8$$

Use the distributive property to multiply 8x+72 by 17.

$$136x+1224-\left(x+9\right)\times 3=8x\times 8$$

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

$$136x+1224-\left(3x+27\right)=8x\times 8$$

To find the opposite of 3x+27, find the opposite of each term.

$$136x+1224-3x-27=8x\times 8$$

Combine 136x and -3x to get 133x.

$$133x+1224-27=8x\times 8$$

Subtract 27 from 1224 to get 1197.

$$133x+1197=8x\times 8$$

Multiply 8 and 8 to get 64.

$$133x+1197=64x$$

Subtract 64x from both sides.

$$133x+1197-64x=0$$

Combine 133x and -64x to get 69x.

$$69x+1197=0$$

Subtract 1197 from both sides. Anything subtracted from zero gives its negation.

$$69x=-1197$$

Divide both sides by 69.

$$x=\frac{-1197}{69}$$

Reduce the fraction \frac{-1197}{69} to lowest terms by extracting and canceling out 3.

$$x=-\frac{399}{23}$$