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February 27th, 2018, 02:20 PM  #1 
Newbie Joined: Jan 2017 From: London Posts: 4 Thanks: 0  Simplify simple expressions
Hi there, Can someone please take a look at the attachment i.e. question 3. I'm going through simplification processes and I understand the two principles to be: 1. Combine like terms 2. Factorize similar terms I've applied this principle exercise 1 and 2 in the attachment but at quite a loss as to how to apply this principle to exercise 3. A step by step procedure to the solution would be much appreciated. Thanks 
February 27th, 2018, 02:58 PM  #2 
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 550 
Rationalize the denominator. $\sqrt{a} + \dfrac{b}{\sqrt{a}} =$ $\sqrt{a} + \left ( 1 * \dfrac{b}{\sqrt{a}} \right )=$ $\sqrt{a}+ \left ( \dfrac{\sqrt{a}}{\sqrt{a}} * \dfrac{b}{\sqrt{a}} \right )=$ $\sqrt{a} + \dfrac{b\sqrt{a}}{\sqrt{a} * \sqrt{a}} =$ $\sqrt{a} + \dfrac{b\sqrt{a}}{a} =$ $\sqrt{a} * \left (1 + \dfrac{b}{a} \right ) = \sqrt{a} * \dfrac{a + b}{a}.$ 
February 27th, 2018, 06:24 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,373 Thanks: 2010 
Or $\displaystyle \sqrt{a} + \frac{b}{\sqrt{a}} = \frac{a}{\sqrt{a}} + \frac{b}{\sqrt{a}} = \frac{a + b}{\sqrt{a}}$, etc.

March 5th, 2018, 04:19 AM  #4  
Newbie Joined: Jan 2017 From: London Posts: 4 Thanks: 0 
I appreciate the step by step follow through Quote:
 

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expressions, simple, simplify 
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