You can put this solution on YOUR website!
This is called a "literal equation." You should start by multiplying both sides by the denominator, and you get this:
Remove the parentheses by distributive property:
You need to get all the 'a' terms on one side and the non-'a' terms on the other side. Subtract 3a from both sides:
ba-3a + 3b= 3a-3a + 2
ba-3a + 3b = 2
Next, get all the NON-'a' terms on the other side by subtracting 3b from both sides:
ba - 3a + 3b-3b= 2-3b
ba-3a = 2-3b
Factor out the common factor of 'a' on the left side, in order to get the 'a' in one place, so you can solve for it:
a(b-3) = 2 - 3b
Finally, divide both sides by (b-3):
or a half dozen other ways to write this answer!!
For a NON-TRADITIONAL explanation of this topic that is probably easier to understand than your own textbook, please see my own website! The easiest way to find it is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the very bottom of this page there is a link that will take you to the Homepage of my website. I have a complete ALGEBRA curriculum there with LOTS of practice tests, and even a few videos. Best of all, it's all FREE!!!
For this particular topic LITERAL EQUATIONS, when you find the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", choose "Intermediate Algebra" and look in "Chapter 2" for "Section 2.07 Literal and Fractional Equations." There is a complete explanation, together with lots of examples and exercises with ALL the answers given. You will especially like the "Math in Living Color" pages that go with this, where hundreds of the hardest exercises are solved for you IN COLOR! I even did a video on this topic before I retired. To see the video, look for "Rapalje Videos in Living Color" on my Homepage, and click on Intermediate Algebra." As I said, everything on this website is FREE! No pop-ups or advertising!!
If you or anyone needs to contact me, my Email address is firstname.lastname@example.org.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus