Question

Solve 1/x-1/x-5=1/3x​

Answer 1

9514 1404 393

Answer:

x = -10

Explanation:

We assume your equation is ...

`(1)/(x)-(1)/(x-5)=(1)/(3x)`

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

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