Question

Solve 1/x-1/x-5=1/3x​

Answer 1

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Answer:

  x = -10

Step-by-step explanation:

We assume your equation is ...

  $\dfrac{1}{x}-\dfrac{1}{x-5}=\dfrac{1}{3x}$

Subtracting the right side, then expressing with a common denominator gives ...

  $\dfrac{3}{3x}-\dfrac{1}{3x}-\dfrac{1}{x-5}=0\\\\\dfrac{2}{3x}-\dfrac{1}{x-5}=0\\\\\dfrac{2(x-5)-3x}{3x(x-5)}=0\\\\\dfrac{-x-10}{3x(x-5)}=0\\\\\boxed{x=-10} \qquad\text{equate the numerator to 0 and add x }$