lim (2/(x-2) + x/(2-x)) as x--2

Question

lim (2/(x-2) + x/(2-x)) as x-->2

anonymous · Answer

attachment

anonymous · Answer

Just showing some of my work there. By just plugging two into the original equation, I got an answer that doesn't exist. Upon trying to simplify the two fractions, I got an indeterminant answer. And wolfram gives me an answer of -1.

zzr0ck3r · Answer

multiply the 1st term by (x-2) and the second by (2-x)
we get lim...(2(x-2)+x(2-x))/((x-2)(2-x)) = lim ... (2x-4+2x-x^2)/(2x-x^2-4+2x) = lim x->2 (4x-x^2-4)/(4x-x^2-4) = lim x->2 1 = 1

zzr0ck3r · Answer

i did something wrong...

anonymous · Answer

I think you just got the terms mixed up. But I did all of that. I simplified the fractions by multiplying by the LCD, as you can see in the picture I posted. The end result of that was "0/0"

zzr0ck3r · Answer

multiply the 1st term by (2-x) and the second by (x-2)
we get lim x->2 (2(2-x)+x(x-2))/(2x-x^2-4+2x) =lim x->2 (-4x+x^2+4)/(4x-x^2-4) = lim x->2 -(4x-x^2-4)/(4x-x^2-4) = lim x->2 -1 = -1

zzr0ck3r · Answer

sorry been a long day...

zzr0ck3r · Answer

make sense @cuzzin ?

anonymous · Answer

Yes, I think I got it. Took me a while, but I think I do get it. Thanks.

zzr0ck3r · Answer

great np