Simplify 5/k + (k+3)/(k+5) .

Given the expression:

E =
5/k  + (k+3)/(k+5)

I am assuming that you need to write the
expression as a single ratio.

Then, we need to determine
the common denominator.

==> E = 5*(k+5) / k(k+5)  +
(k(k+3) / k(k+5)

Now we will open the
brackets.

==> E = (5k+25)/(k^2+5k)  + (k^2 + 3k)/
(k^2 + 5k)

==> E = (5k+25+ k^2 + 3k) /
(k^2+5k)

Now we will combine like
terms.

==> E = (k^2+8k+ 25) / (k^2 +
5k)