In this example, we're going to solve
an equation using the quadratic formula.
Let G of X equal 2 over X
plus two over X plus 3. Find all
X for which G of X equals one. The first
thing we're going to do is replace
G of X with 1. Notice that we have
an equation involving
rational expressions.
When you're working with a problem
such as this, what we can do is we can
multiply everything
by the least common denominator. In this
case, the least common denominator is
going to be X
times X plus 2. Remember, it's the
product of
all unique factors, each raised to its
highest exponent.
Since we only have two unique factors,
it's just simply the product of the two.
So let's multiply everything by that LCD
On the left-hand side, we have X squared plus 3x.
I went ahead and distributed the X. In
our first term,
we see that X and X cancel out, leaving me
with 2x plus 6. And again, I went ahead and distributed that two.
Plus,
here, the X plus threes cancel out,
leaving me with 2x. Now let's combine our like terms.
Now I'm going to subtract
everything from the right hand side
so that I can set it equal to 0.
Now that I have my quadratic equation, I
can label my a, b, and c
and replace it
in my quadratic formula. A
is 1, b is -1,
c
is -6. So, let's replace
our variables and simplify.
Negative b would be a positive 1,
-1 squared is a positive one, -4
times 1 times -6 gives me a positive
24, two times 1 is just 2,
1 plus 24...
Now we can take the square root of 25 
and now we'll need to break this up into two answers.
We have 1 plus 5
over 2, 1 minus 5 over 2. 
So the first one would give me
6 divided by 2, which is
3; the second one would give me -4
divided by 2, which is -2. So these
are my answers.
