Solving for x (this should be easy but somehow I keep messing it up)

[ilovemynny]

Intro:
I'm starting college this fall. I asked one of my professors if we had a textbook and he said that there's an online version and I should read a bit of it if I wanted to.
On the first chapter they were talking about simple (I mean really simple algebra, this is a vector geometry class) but I got completely stumped on one of the problems.

I got an answer but it seems to be different from the textbook answer. I tried putting in number valves for the variable in the 2 different solution but i got different solutions. I probably did this wrong s0 can someone help me solve this I don't want to be stumped on my first week of college with the engineers >.<

Problem:
It should be uploaded on this message as an attachment.

What I Did:

called "problem my way" attachment

Supposed Answer: attachment called "answer"

 

[eumyang]

You're answer is the same as the given solution. You just have to clean your expression up a bit.
x = \frac{e}{\frac{c - a}{a + 1/b} - d} - c
Take the fraction in the denominator and multiply by \frac{b}{b}
x = \frac{e}{\frac{b(c - a)}{ba + 1} - d} - c
Perform the subtraction in the denominator by finding the LCD (which is ba + 1):
x = \frac{e}{\frac{b(c - a)}{ba + 1} - \frac{d(ba + 1)}{(ba + 1)}} - c
x = \frac{e}{\frac{b(c - a) - d(ba + 1)}{ba + 1}} - c
Multiply the entire fraction by \frac{ba + 1}{ba + 1}
x = \frac{e(ba + 1)}{b(c - a) - d(ba + 1)} - c


Note to mods: I don't think I'm giving too much away here. This is not in the HW subforum and the OP did show a lot of the work.

 

[GarageDweller]

I find it useful to do some substitutions when solving these, you could clean up the expression given and make things a lot easier

 

[ilovemynny]

Oh, THANK YOU! I tried using substitution to check but yeah since it's so messy I probably messed up somewhere. Thank you so much! This problem was really starting to freak me out. Thank you, eumayang, for cleaning it up! I tried converting my answer to the book's answer but I was really confused on how to do it.