Question 780379: Please help me solve this equation:
Thank you!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
No one can help you solve an equation unless you provide an equation to solve. The word "equation" has a specific meaning, and that meaning is not "a bunch of math-looking stuff". It means exactly this: "Two expressions related by an equals sign."
as complex as it is, is just a single expression and there is no equals sign to be seen anywhere.
Now just on the off chance that what you really meant to say is "Please help me simplify this expression, then read on.
You need to rationalize the denominator. Since you have a binomial expression in your denominator, squaring it won't do anything for you since you will still have a radical in the denominator expression. What you need to do is multiply the denominator by the conjugate of the denominator. What's a conjugate? If you have a binomial  then its conjugate is  .
The trouble is, you can't just willy-nilly multiply a denominator that is something different from 1 without changing the value of the fraction. But you can multiply the ENTIRE fraction by 1 in the form of the conjugate of the denominator divided by itself. Thus:
\left(\frac{\sqrt{t}\ +\ 4}{\sqrt{t}\ +\ 4}\right))
This works because the product of a binomial and its conjugate is the difference of two squares.
And since  does not evenly divide  , you are done.
And, despite the fact that the finished product might look more complex than the original, the fact that there is no radical in the denominator makes it simpler by definition.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
|
|
|
