9514 1404 393
Answer:
x = -10
Step-by-step explanation:
We assume your equation is ...
[tex]\dfrac{1}{x}-\dfrac{1}{x-5}=\dfrac{1}{3x}[/tex]
Subtracting the right side, then expressing with a common denominator gives ...
[tex]\dfrac{3}{3x}-\dfrac{1}{3x}-\dfrac{1}{x-5}=0\\\\\dfrac{2}{3x}-\dfrac{1}{x-5}=0\\\\\dfrac{2(x-5)-3x}{3x(x-5)}=0\\\\\dfrac{-x-10}{3x(x-5)}=0\\\\\boxed{x=-10} \qquad\text{equate the numerator to 0 and add $x$}[/tex]
