Question 845307: My textbook for Algebra asks for us to "Solve the equation" but our teacher didn't go over this and I'm confused. The problem in question is  am I supposed to use the quadratic formula for this? Thanks for your trouble!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You could go about it one of two ways:
1) You could multiply both sides of the equation times  to get
 <-->  and solve that equation.
(That is probably the expected way).
2) You could say  , and that makes  ,
and substituting you would get
 .
Solving that equation you get solutions for  ,
which you can substitute into to find the values for  .
MULTIPLYING TIMES :
We know that is not zero, because it is in a denominator and if it were zero,  would not exist. If we found  as a solution, we would discard it, because we know it is not a valid solution of
.
So we can safely multiply times both sides of the equal sign.will get
The quadratic formula says that the solutions to
 are given by
is with
 ,  , and  .
So 
The solutions are
 and 
NOTE:
You could use the quadratic formula, or you could solve by factoring, or you could even solve by completing the square.
For , using the quadratic formula is very reasonable,
because the other options do not seem any easier.
If you had changed variables (option 2) above) to end with
,
you may find that factoring is the easiest option.
You may immediately see that you can factor to get
 ,
which would tell you that the solutions are  and  .
means  -->  --> --> 
means  -->  --> --> 
|
|
|
