Multiplying Rational Expressions

[King Friday]

The given problem with the instructor's solution is on top.
My approach to the answer is below. I'm just not seeing how I get to the instructor's answer.
Any guidance here would really be appreciated!
Thanks in advance.

 

[fresh_42]

[math]\begin{array}{lll} \dfrac{2a^2+6a}{18a^2}&=\dfrac{2a\cdot (a+3)}{2a\cdot 9a}=\dfrac{\sout{2a}\cdot (a+3)}{\sout{2a}\cdot 9a}=\dfrac{a+3}{9a} \end{array}[/math]or easier if you start with cancelling [imath] 2a [/imath] across the two quotients
[math]\begin{array}{lll} \dfrac{2a}{3}\cdot \dfrac{a+3}{6a^2}&=\dfrac{2a}{3}\cdot \dfrac{a+3}{2a\cdot 3a}=\dfrac{\sout{2a}}{3}\cdot \dfrac{a+3}{\sout{2a}\cdot 3a}=\dfrac{a+3}{9a} \end{array}[/math]

 

[khansaheb]

The given problem......

You did not tell us :

What is it that you need to accomplish!!

 

[The Highlander]

You did not tell us :

What is it that you need to accomplish!!

Er, I believe he made it quite clear what he wished to accomplish and @fresh_42 ably helped him do so.

 

[khansaheb]

Er, I believe he made it quite clear what he wished to accomplish and @fresh_42 ably helped him do so.

Did the query "wanted" to be shown that

LHS = RHS.............................Not explicitly asked for.

That can be accomplished in multiple (different) ways.

 

[fresh_42]

I showed how one gets from his result to the book result, and how the book result is achieved more easily. I don't think there can be added anymore without a dialogue with the OP.