How Do You Divide Rational Expressions?

[tikka]

hello people. I am sorry about this post becuse i have been reading some of the posts here and they are really high lvl math. I however am only in grade 10. I am having troubles dividing rational expressions. I have missed a week or so of school and I am lost now
. i have an example here that hopefully some one can walk me step by step through it.
Thanks for your time and posts are appreciated.


EX.
x^2 - x - 20 x^2 + 9x + 20
------------- / --------------
x^2 - 6x x^2 - 12x + 36

i can't seem to get them to tay where i put them so the bold is on the right side and the normal is on the left

 

[mathman]

hello people. I am sorry about this post becuse i have been reading some of the posts here and they are really high lvl math. I however am only in grade 10. I am having troubles dividing rational expressions. I have missed a week or so of school and I am lost now
. i have an example here that hopefully some one can walk me step by step through it.
Thanks for your time and posts are appreciated.


EX.
x^2 - x - 20 x^2 + 9x + 20
------------- / --------------
x^2 - 6x x^2 - 12x + 36

i can't seem to get them to tay where i put them so the bold is on the right side and the normal is on the left

I have trouble understanding what your expressions mean. However, the general idea of dividing a polynomial by another polynomial is very much like doing long division.

For example (assuming you want (x^2 - x - 20)/(x^2 - 6x)) first look at the highest degree terms in the numerator and the divisor and divide. In this case it is 1. Then multiply the divisor by the trial quotient and subtract from the numerator to get the next trial numerator. Keep going until the trial numerator is of lower degree than the divisor. This last trial numerator is the remainder. In this example, the quotient is 1 and the remainder is 5x - 20.

 

[Evalesco]

Hi tikka,
If you are doing algebraic long division like mathman suggested then I think the following sites will be useful to you:

1) http://www.rfbarrow.btinternet.co.uk/htmasa2/AlgDiv1.htm
It has a java applet which will step you through the process.

2) http://en.wikipedia.org/wiki/Polynomial_long_division
Wikipedia has quite a good entry on the topic, they call it polynoimal long division but it is the same process.

 

[symbolipoint]

Tikka,

Learn to use tex or TexAide to write (or "type") your expressions to appear in a conventional notated form. TexAide is a free download and is easy to use.

To divide rational expressions, you use the same process as you use for numeric constants - no change. Watch this:

$$\[ \begin{array}{l} \frac{{x^2 - x - 20}}{{x^2 - 6x}} \div \frac{{x^2 + 9x + 20}}{{x^2 - 12x + 36}} \\ \\ \frac{{x^2 - x - 20}}{{x^2 - 6x}} \bullet \frac{{x^2 - 12x + 36}}{{x^2 + 9x + 20}} \\ \frac{{(x - 5)(x + 4)}}{{x(x - 6)}} \bullet \frac{{(x - 6)(x - 6)}}{{(x + 4)(x + 5)}} \\ \end{array} \]$$

You see, back factoring any factorable expressions, here you find simplification is possible, or hopefully, helpful.

Then you obtain:

$$\[ \frac{{(x - 5)(x - 6)}}{{x(x + 5)}} = \frac{{x^2 - 11x + 30}}{{x^2 + 5x}} \]$$

Can you take it from there, or still need help? You want to use the expression on the right side, since it is simplified and in a good multiplied form (general forrm).