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

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) (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...
RELATED QUESTIONS
F is given. Find all values of a for which f(a) is the indicated value.... (answered by MathLover1,Edwin McCravy)

Let f(x) = (floor(x(floor x) for x >= 0. (a) Find all x >= 0 such that f(x) = 1.... (answered by greenestamps)

help is appreciated! Let $f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for x >= 0... (answered by ikleyn)

x 0 1 2 3 f(x) 1 2 5 10 The table above... (answered by ewatrrr)

F(x)=-6/x-3-1......for which values of x is f(x)... (answered by Alan3354)

given set Z(26) = {0,1,2,3,...25} Let a and b be integers. Consider the function f:... (answered by ikleyn)

Let f(x) = (4x - 1)/(5x + 2) + x/(x + 5). For what value of a is f(a) =... (answered by mananth)

I am having trouble with function notation. Please help! Q1. Let f(x)=x^2-1,... (answered by solver91311)

If f(x-1)=x+1 for all the values of x which of the following is equal to f(x+1) ? A)... (answered by Fombitz)