Hey guys, so I’ve attached a picture where Greg has said x would always be greater than -2, as he took two cases (0 and 2) and worked with those, getting the result. However, if I were to plug in x=-3, I would still not get a 0 in the denominator. So shouldn’t the answer be C, cannot be determined? Or have I got the concept all wrong? Because I didn’t completely understand why Greg took 0 and 2 in particular.
Thanks!
Hi Shreyas,
I am still a beginner in GRE. But, as far as the concept goes for this question, the roots of this given equation will be either 0 or 2.
Regardless of what is given in the denominator, all that matters is what values of “x” you get by solving the quadratic equation.
In this case, by solving, you will get either 0 or 2. And 0/2 both are greater than -2. Hence, A.
If there is any better explanation or correction, you are most welcome to do so
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Here RHS=0 means only the numerator can be 0. If the denominator is 0 then the answer would be undefined(Since anything divided by 0 is an undefined quantity). So x(x-2)=0 i.e., either x = 0 or x =2. So for both cases A >B.
Coming to your doubt, if you plug in x =-3 then the denominator will automatically become 0(x+3 case).
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Oops, I just realised I REALLY misread the question haha, really sorry, thank you so much for all the help!