SOLUTION: let f(x) = 1/x+1 + 3/x-5 find all values of "a" for which : f(a) = f(a+6)

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Question 39769: let f(x) = 1/x+1 + 3/x-5
find all values of "a" for which : f(a) = f(a+6)
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Given f(x) = 1/x+1 + 3/x-5
we wish to find f(a) amd f(a+6) and set them equal...thus finding what values of a make it so, so we have
f(a) = 1/(a+1) + 3/(a-5) and
f(a+6) = 1/(a+7) + 3/(a+1)
so we need to solve
1/(a+1) + 3/(a-5) = 1/(a+7) + 3/(a+1)
Multiply all by the LCD (a+1)(a-5)(a+7) and get
(a-5)(a+7) + 3(a+1)(a+7) = (a+1)(a-5) + 3(a-5)(a+7)
subtract off the (a-5)(a+7) and get
3(a+1)(a+7) = (a+1)(a-5) + 2(a-5)(a+7)
and now work it out
3a^2 + 24a + 21 = a^2 - 4a - 5 + 2a^2 + 4a -70
24a + 21 = -75
24a = -96
a = -4
good algebra 2 problem...I like that one...