SImplify the expression?

Question

Simplify the expression into a single fraction of the form
Numerator/Denominator ,and determine the numerator and the denominator as functions of
u. (You do not have to factor the numerator and do not cancel any terms between the numerator and denominator.)

(9 )+ (1/u)+(6/1u+5)

Answer 1

Hi Aleses

 

(9 )+ (1/u)+(6/1u+5)

 

I'm going to rewrite this to make the work a bit clearer

 

        1             6

9 + ---- + ----------

        u          u+5

 

The first thing we need to do is determine the common denominator.

 

It this case, it is (u)(u+5)

 

     u(u+5)      1    (u+5)        6      u

9 • -------- + -- • ------- + ------ • --

     u(u+5)     u    (u+5)      u+5    u

 

9u(u+5)      u+5          6u

--------- + -------- + --------

 u(u+5)    u(u+5)     u(u+5)

 

9u²+45u + u+5 + 6u

------------------------

        u(u+5)

 

9u² + 52u + 5

---------------- 

      u(u+5)

 

9u2 + 52u + 5
----------------
     u²+5u