, right? Notice that I just multiplied the left summand and the right summand by 1 because and . Since all I did was multiply by one, nothing has really changed. But now, multiplying the fractions together, you have a common denominator which is . The only other thing I did was take the negative sign on the second summand and put that outside the fraction, making it subtraction rather than addition.
Now that we have , we can get
and you can multiply the denominator out if you want to.
LaTeX is a compiling program/language... I don't know.
LaTeX is a thing that lets you make pretty math symbols. If you have Windows 7 it's probably already on your computer, under the name TeXWorks. If you have a Mac you may have to download a program that lets you use LaTex, and if you have Linux you can just do a search for a LaTeX program--most people seem to like MikTex.
The way it works is this: Open a VERY simple document file type, like .txt. Whatever it is, it can't do a lot of formatting for you. When you open it, you paste in some beginning commands. My opening commands look like this:
\documentclass[12pt,letterpaper,final,oneside]{article}%article, letter, report, book
\usepackage{amscd}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[pdftex]{graphicx}
\usepackage{amsmath}
\usepackage{setspace}
\usepackage{verbatim}
\usepackage{ulem}
\usepackage{booktabs}
\usepackage{natbib}
\bibpunct{(}{)}{;}{a}{}{,}
\usepackage{graphicx}
\DeclareGraphicsExtensions{.pdf,.png,.jpg}
\usepackage{fancyhdr}
\addtolength{\oddsidemargin}{-.8in}
\addtolength{\evensidemargin}{-.6in}
\addtolength{\textwidth}{1.2in}
\addtolength{\topmargin}{-1in}
\addtolength{\textheight}{1in}
\usepackage{palatino, url, multicol}
\usepackage{enumerate}
\usepackage{multirow}
\usepackage{color}
\parindent=.35in
\newcommand{\HRule}{\rule{\linewidth}{0.5mm}}
\newcommand{\JRule}{\rule{0.67\linewidth}{0.025mm} }
\newcommand{\verteq}[0]{\rotatebox{90}{$=$}}
%To produce a vertical =, \verteq
%To produce Helvetica, {\fontfamily{phv}\selectfont ...}
%To manipulate footnote symbols, {\renewcommand{\thefootnote}{\fnsymbol{footnote}} ... \footnote{...} ... }
%To produce a ~, \sim
%To produce a picture, save the file .png to the same folder as the .tex file, and insert command \includegraphic{...png}
%\! deletes a small space, \, adds one, \; adds a normal space, \: a large one
%To produce enumerated lists, use \begin{enumerate}... \item ... To set the counter, use \begin... \setcounter{enumi}{0} \item ... to set at the first level, setting to 0. For unenumerated lists, just \begin{itemize} \item...
%Not equivalent, \not\equiv
%To end pagenotes, \pagestyle{empty}
%Entails is \vdash, reverse is \dashv
\begin{document}
Don't worry about what all that means, just paste it into each document to start yourself off. Then, after the \begin{document} line, you can start typing and everything is beautiful. When you want to enter math symbols, you have to enter a "math mode". You can do this by using just $$. For instance, to make you write $5 \times 7$. Another way to enter math mode is to type \begin{align} \end{align}. This will center your math text. So you would type \begin{align} 5 \times 7 \end{align}.
From there you can learn all kinds of symbols, including the ones for fractions.
That's the long story about LaTeX in general. The LaTeX used in these forums is much simpler. When you write something, make sure you're in "advanced mode". Whenever you want to type LaTeX commands, just surround the text with [ M A T H ] [ / M A T H ] without any of the spaces (or just click the button that says TEX) and type what you want to type. If you see someone who has made a cool LaTeX thing and you want to know how to do it, just double-click on the stuff and it'll show you the code that was used to produce it.
It makes your writing look much nicer. If you take advanced college courses in mathematics, professors will encourage you to use LaTeX. If you get university degree in mathematics you will need to write a piece of original research which must be produced in LaTeX. If you publish anything in the sciences or mathematics, it must be produced in LaTeX.
If you're not going to go very far beyond calculus, though, you'll never really need it.
Okay, yeah, if you're looking for money then you're not going to be researching math or science, and you won't need LaTeX. Mech engineers use math that goes only a little bit beyond calculus. They use differential equations, linear algebra, ... and that's about all I can think of. Your math life shall be easy and boring.
Well, I'm speaking a little bit over your head because you've not yet seen real math. Mech engineers will use the kind of stuff you're studying right now all the time, so if you like that stuff don't worry. However, as you get older and have a better grasp of what's going on, the whole thing will seem so obvious that it's boring. But by that time you'll be an engineer and you'll have (hopefully) interesting non-mathematical challenges, like: How do I take these wires and pipes and make a thing that does a job, which my customer wants it to do? Sure, you'll use math for some of that. But the interesting part will be using some intuitions and reasoning skill about how to solve a physical problem--and that's not exactly math. (Well, this kind of problem is interesting to some people. I find it boring, but I love math and math alone.)
Depending on what kind of accounting you do, you might use some semi-serious math. Quantitative finance people make TONS of money and their average salaries are only getting bigger as time goes on--and they use serious math.