If m>0 and n>0, is m+x/n+x > m/n?

[anoo.anand]

If m>0 and n>0, is m+x/n+x > m/n?

1) m< n

2) x > 0

What is the better approach ? plluging numbers or solving ?

[goelnikhils]

I think the answer should be 'C'

There is no need to plug numbers . It is given m<n in A and both m & n >0 so now we need to know about X , it says X>0 .

[sunny.jain]

IMO:C

No need to plug in numbers...solve it like this

m+x/n+x -m/n > 0

x*(n-m)/n*(n+x) > 0

for this to be positive, we need
either numerator and denominator both +ve or both -ve.

we know only one thing: n = +ve
we need sign of X, (N-M), and (N+X) ?

A) m< n ==> N- M == +ve
still we need two more sign.

B) X > 0 ==> X is +ve and N+X is +ve as N is +ve.
But again we dont know the sign of N-M.

combine these two, we get all we want. So answer is C.

[Ben Ku]

Good approach, Sunny. Let me know if anything's unclear or if you have any other questions relating to this problem.

[lh.abhishek]

Good approach, Sunny. Let me know if anything's unclear or if you have any other questions relating to this problem.

can u please tell me, when i do i decide to take the numbers to other side? like sunny did here ??

should always do it ??

[Ben Ku]

When you have an algebraic equation or inequality, it's usually helpful to have everything on one side, because then you can compare it to zero.

Here are three examples:

If you have x^2 - 6 = x, placing everything on one side gives you x^2 - x - 6 = 0. We can factor it to get (x - 3)(x + 2) = 0. either x - 3 = 0 or x + 2 = 0, so x = -2 or 3.

If you have x^3 -6x = x^2, it's tempting to divide everything by x. However, you should never divide equations by a variable (unless you know it's not zero). The approach here is also bring everything to one side: x^3 - x^2 - 6x = 0, and simplify from there: x(x - 3)(x + 2) = 0, so x = -2, 0, or 3.

If you have x^2 - 6 > x, we can place everything on one side getting: x^2 - x - 6 > 0 or (x - 3)(x + 2) > 0. Here, we see that because (x - 3)(x + 2) is positive, then either (x-3) and (x + 2) are both positive or both negative. Only numbers less than -2 or greater than 3 will work.

Hope that helps.