Hi dmatinho,
The factoring involved in this question is a bit more complicated than normal since we're factoring out a "term" and not just an individual number or variable.
For example, factoring the following is pretty easy:
2X - 4
2(X - 2)
Since you can "see" that there's a "2" in both terms
In this prompt, we have to factor out (2T-1) from each of the terms:
[(2T-1) + (2T-1)^2]/(2T-1)
I'm going to split the numerator into 2 'pieces'....
(2T-1) and (2T-1)^2
Now, think about how you would factor (2T-1) out of each piece...
(1)(2T-1) and (2T-1)(2T-1)
Next, when we completely factor out (2T-1), think about what's "left over"....
(2T-1)[ (1) + (2T-1)]
Inside the bracket, the +1 and the -1 'cancel out', leaving us with...
(2T-1)(2T)
The last step is to deal with the denominator of the original fraction....
(2T-1)(2T)/(2T-1)
That denominator cancels out the same term in the numerator, leaving us with....
2T
The approach that you took is fine; you're ultimately just breaking the fraction into two pieces and then combining the results later.
GMAT assassins aren't born, they're made,
Rich
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