Question

A rational function g is given below. Find all values of a for which g(a)=12.

g(x)= 4/x+3 + 16/x^2+6x+9

Answer 1

\[4/a+3+16/a^2+6a+9=12\\
\frac{4a+16}{a^2}=0\\
a=4
\]

Answer 2

4/(a+3) + 16/(a+3)^2 = 12
4[1/(a+3) + 4/(a+3)^2] = 12
now taking lcm
(a+3)+4= 3(a+3)^2
simplifying
3a^2 +17a +20 = 0
now using the quadratic formula to find the roots we will get
a = -4 or -5/3

Answer 3

thats what the question says?

Answer 4

yea