Question

If f(x)=3(x+5)+4/x, what is f(a+2)

Answer 1

Let's plug a + 2 in for x.

`f(x)=3(a+2+5)+ (4)/((a+2))`

`f(x)=3a+21+ (4)/(a+2)`
Now here comes the hard part; we have to find the common denominator between rational expressions!

`f(x)= (3a)/(1) + (4)/(a+2) +21`

`f(x)= (3a(a+2))/(a+2) + (4)/(a+2) +21`
See what I did there? Now we have common denominators, and the values are still the same ;)

`f(x)= (3a^2+6a)/(a+2) + (4)/(a+2) +21`

`f(x)= (3a^2+6a+4)/(a+2) + (21(a+2))/(a+2)`
Did the same thing for 21.

`f(x)= [tex]f(x)=(3a^2+27a+46)/(a+2)`[/tex]
Here is what I got. It is always helpful to check work, however. I couldn't factor the top quadratic equation. Hope this helps!