SOLUTION: Add. Express your answer in simplest form. Must show the algebraic steps to solve for x in order to get credit. 4x/x^2+18x+72 + 4/x+6 = ????? I have come up with 2/x+3, b

Question 65829: Add. Express your answer in simplest form. Must show the algebraic steps to solve for x in order to get credit.
4x/x^2+18x+72 + 4/x+6 = ?????
I have come up with 2/x+3, but I am not sure if I need to do more with the answer to solve for x??? Would I have to do something like:
2/x+3 = 0. If so, I think I am stuck on this one!!! If anyone has the time, I sure would appreciate a little help with this problem. Thanks.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4x/x^2+18x+72 + 4/x+6
The lcd is (x+6)(x+12)
Rewrite each fraction with the lcd as its denominator, as follows:
=[4x/lcd]+[4(x+12)/lcd]
Combine the numerators and write over the lcd, as follows:
=[4x+4(x+12)]/lcd
Simplify the numerator, as follows:
=[8x+48]/lcd
Factor the numerator:
=[8(x+6)]/[(x+6)(x+12)]
Cancel the common factor (x+6) to get:
=8/(x+12)
Cheers,
Stan H.
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