Algebra Question Bank, Q16

[caa8q]

Hi all,

I have a question regarding MGMAT's Alegebra Question Bank, #16.

I recommend that you write it out bc it may be hard to read with all the parentheses.

If x and y are nonzero integers, is [(x^-1) + (y^-1)]^-1 > [(x^-1)(y^-1)]^-1 ?

(1) x = 2y

(2) x + y > 0

My question is about how to simplify the actual question we are asked. The explanation says:

[(x^-1) + (y^-1)]^-1 > [(x^-1)(y^-1)]^-1
[(1/x) + (1/y)]^-1 > (1/xy)^-1
[(x+y)/xy]^-1 > xy
xy/(x+y) > xy

How do you get from the red step (line 2 above) to the blue step (line 3 above)?

Btw the answer is (A).

Thanks in advance for your help!

[jlucero]

Short answer: common denominators

Long answer:
(1/x) + (1/y)
y/xy + x/xy
(x+y)/xy

[caa8q]

Thanks!

[RonPurewal]

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