Question

Please solve equation for x with steps 1/3x= 1/3+ 6/x

Answer 1

The given equation is

$\frac{1}{3}x=\frac{1}{3}+\frac{6}{x}$

First, we subtract 6/x on each side

$\frac{1}{3}x-\frac{6}{x}=\frac{1}{3}+\frac{6}{x}-\frac{6}{x}\rightarrow\frac{1}{3}x-\frac{6}{x}=\frac{1}{3}$

Second, we solve the difference in the left side of the equation

$\frac{x^2-18}{3x}=\frac{1}{3}$

Third, we simplify numbers 3, and multiply the equation by x

$\frac{x(x^2-18)}{x}=x\rightarrow x^2-18=x$

Fourth, we subtract x on each side to get the quadratic equation

$x^2-18-x=x-x\rightarrow x^2-18-x=0$

Additionally, we need to find two number which product is 18, and which difference is 1. Those numbers are no integers, so, we must use a calculator.

Using a calculator, the solutions are

$x_1=4.77,x_2=-3.77$