# Rational Expressions & Quadratic Formula Help

• Aug 31st 2007, 09:13 AM
unreal030
Rational Expressions & Quadratic Formula Help
Hey guys I need some help with a problem. I am in a required math business class at college and I and we are doing some review first. Its completely online, I haven't taken any math since Algebra 2 first half of my junior year in High School, so I have forgotten most of it. Seems like most of my class mates are in the same boat since they are of no help.

At any rate, I have gotten through everything except for 2 problems. The book, as usual is of no help so...

If you could explain these two problems to me I would really appreciate it, and I mean every single step, thats usually how the book has been unhelpful. On the offchance it has a similarly formatted problem, the one part where they do something and get this wild number I can't figure out how they went about getting it.

I know these help forums don't usually like "doing" peoples homework. However, this system they use is called MapleTA online, you do the homework, you can do it an unlimited # of times. You don't get a gradesheet (only includes answers, no explanation) once you finalize your HW session. If you want to do it again, it gives you similar problems but all new numbers and maybe slightly differently organized, so this is just so I know how to go through the process when I go through it again.

Write each expression as a single power of X.

Don't know how to write this on the computer, unlike all of the other stuff but basically its:

x^1/2 over x^1/3 , it is in a single, large parenthesis. Then, in exponent form right outside of the parenthesis is 1/3.

Next problem is quadratic formula. I am frustrated with this because I used to be able to do it. I get about halfway through, and I get stuck.

3x^2+2x-4=0

Basically this is what I do:

x=2 plusorminus sqroot 4-4 over 2

since 4-4=0, do I just eliminate that? that only leaves 2+- over 2, what would be my answer??

Since that is a little different then some of the other quadratic problems because of the 0, could someone tell me how you get a certain numbers from this example I found in the book??

X^2-2x-1=0

they do:

-(-2) plusorminus sqroot(-2)^2-4(1)(-1) over 2(1)

no problem with that. but then they get this, and don't explain how. basically the sqroot stuff is confusing me. I used to know this but once again, I have forgotten, so the whole (random number)sqroot(random num) confuses me as far as how they got there from the above.

=2 plusorminus sqroot 8 over 2 = 2 plusorminus 2sqroot2 over 2

Thank you again in advance. I appreciate it.
• Aug 31st 2007, 09:38 AM
Krizalid
$\displaystyle ax^2+bx+c=0$ it's solved with $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Even sometimes is not necessary to apply it ('cause you can factorice the equation).
• Aug 31st 2007, 10:25 AM
unreal030
yeah I already know the formulas and all of that. I am just getting stuck halfway through because I have forgotten something else from before learning that it seems and I can't recall that part of the operation.
• Aug 31st 2007, 10:45 AM
Jhevon
Quote:

Originally Posted by unreal030
Write each expression as a single power of X.

Don't know how to write this on the computer, unlike all of the other stuff but basically its:

x^1/2 over x^1/3 , it is in a single, large parenthesis. Then, in exponent form right outside of the parenthesis is 1/3.

is this what you mean?

$\displaystyle \left( \frac {x^{1/2}}{x^{1/3}} \right)^{1/3} =$ ?

in any case, here are the rules you need to know for this:

$\displaystyle \frac {x^a}{x^b} = x^{a - b}$

$\displaystyle \left( x^a \right)^b = x^{ab}$

Quote:

3x^2+2x-4=0
let's go through it.

by the quadratic formula, we have:

$\displaystyle x = \frac {-2 \pm \sqrt {4 - 4(3)(-4)}}{6}$ ......................just applied the formula

$\displaystyle \Rightarrow x = \frac {-2 \pm \sqrt {52}}{6}$ ................................calculate what is under the square root

$\displaystyle \Rightarrow x = \frac {-2 \pm 2 \sqrt {13}}{6}$ ...............................simplified the square root using a knowledge of surds

$\displaystyle \Rightarrow x = - \frac {1}{3} \pm \frac {\sqrt {13}}{3}$ ...............................(optional) split the fraction up

any questions? if not, try some more and let me see your solutions