Solve 1000/x12=1600/x+3

$$\frac{ 1000 }{ x } 12 = \frac{ 1600 }{ x+3 }$$

Solve for x

$$x = -\frac{45}{13} = -3\frac{6}{13} \approx -3.461538462$$

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.

$$\left(x+3\right)\times 1000\times 12=x\times 1600$$

Multiply 1000 and 12 to get 12000.

$$\left(x+3\right)\times 12000=x\times 1600$$

Use the distributive property to multiply x+3 by 12000.

$$12000x+36000=x\times 1600$$

Subtract x\times 1600 from both sides.

$$12000x+36000-x\times 1600=0$$

Combine 12000x and -x\times 1600 to get 10400x.

$$10400x+36000=0$$

Subtract 36000 from both sides. Anything subtracted from zero gives its negation.

$$10400x=-36000$$

Divide both sides by 10400.

$$x=\frac{-36000}{10400}$$

Reduce the fraction \frac{-36000}{10400} to lowest terms by extracting and canceling out 800.

$$x=-\frac{45}{13}$$