SOLUTION: Let f(x) = (4x - 1)/(5x + 2) + x/(x + 5). For what value of a is f(a) = 3?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Let f(x) = (4x - 1)/(5x + 2) + x/(x + 5). For what value of a is f(a) = 3?      Log On


   

Question 1209315: Let
f(x) = (4x - 1)/(5x + 2) + x/(x + 5).
For what value of a is f(a) = 3?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = (4x - 1)/(5x + 2) + x/(x + 5).
For what value of a is f(a) = 3?
f%28x%29+=+%28%284x+-+1%29%2F%285x+%2B+2%29%29+%2B+%28x%2F%28x+%2B+5%29%29

f%28a%29+=+%28%284a-+1%29%2F%285a+%2B+2%29%29+%2B+%28a%2F%28a+%2B+5%29%29


%28%284a-+1%29%2F%285a+%2B+2%29%29+%2B+%28a%2F%28a+%2B+5%29%29=+3
multiply equation by (5a+2)(a+5)
(4a-1)(a+5)+a*(5a+2) =3(5a+2)(a+5)
=
4a^2+19a-5+5a^2+2a = 15a^2+81a+30
9a^2+21a-5 = 15a^2+81a+30
6a^2+60a+35 =0
SUse formula method
a= 6 , b= 60 ,c = 35
b^2-4ac = 60^2- 4*6*35 = 3600-840 =2760
a+=+-%28b+%2B-sqrt%28b%5E2-4ac%29%29%2F2a


a+=+%28-60+%2B-+sqrt%282760%29%29%2F12+

a+=+%28-60%2B-2%2Asqrt%28690%29%29%2F12+

a=+%28-30+%2B-sqrt%28690%29%29%2F6