So simplify 5/k + (k+3)/(k+5), we make the denominator the same for all the terms

5/k+(k+3)/(k+5)

=> [5(k + 5) + k(k+3)]/ k(k+5)

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

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

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

** The required result is (k^2...**

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So simplify 5/k + (k+3)/(k+5), we make the denominator the same for all the terms

5/k+(k+3)/(k+5)

=> [5(k + 5) + k(k+3)]/ k(k+5)

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

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

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

**The required result is (k^2 + 8k + 25)/(k^2 + 5k)**

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)**