Question

How to solve this equation

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

Answer 1

1/5 ( 1/3X - 5 ) = 1/ 3 ( 3 - 1/ X)


1/15X - 1 = 1 -1/3X Simplify both sides.

15X( 1/ 15X - 1 ) = 15X ( 1 - 1/3X)

1 - 15X = 15X -5

6 = 30X

X = 6/30 = 1/5


Alternate solution

1/5(1/3x-5)=1/3(3-1/x) to find x simply multiply both sides of equation by the LCM for 3,5 (15), then solve:

So,

(15)times 1/5(1/3x-5)=(15)times 1/3(3-1/x) implying 3(1/3x-5)=5(3-1/x) leading to 1/x-15=15-5/x

Now isolating the monomial we get 5/x+1/x=30 leading to 6/x=30; dividing both sides by 6 gives 1/x=5 and
finally x=1/5.