What are the four integral values of x for which x/(x-2) has an integral value?

x/(x-2)

1 Answer

The integer values of x are 1,3,0,4

Explanation:

Lets rewrite this as follows

x/(x-2)=[(x-2)+2]/(x-2)=1+2/(x-2)

In order for 2/(x-2) to be integer x-2 must be one of the divisors of 2 which are +-1 and +-2

Hence x-2=-1=>x=1
x-2=1=>x=3
x-2=-2=>x=0
x-2=2=>x=4

Hence the integer values of x are 1,3,0,4