1.4 Fractional Expressions

Why hello:) Today, I am going to inform you on FRACTIONAL EXPRESSIONS *insert excitement here*

First and most importantly, a FRACTIONAL EXPRESSION is a quotient of two algebraic expressions.
a special case is RATIONAL EXPRESSION: is a quotient p/q of two polynomials p and q. Since division by 0 is not allowed, domain p/q consists of all real numbers except those that make the denominator 0.

Simplification Process: Common nonzero factor in the numerator and denominator of a quotient may be canceled!

Simplify rational expressions:

is simplified if numerator and denominator h

ave no common polynomial factors of positive degree and no common integral factors greater than 1. EXAMPLE BELOW

Products and quotients of rational expressions:

This is pretty basic stuff. You multiply the two fractions together using the property of quotients, like we did in 1.3- then you factor all polynomials, and cross out the thins you can (simplification process) then you should have you answer with the "if x does not equal this" in subscript above it! I'm not doing an example because it's just like simplifying rational expressions, just with an added multiplication step at the beginning!

To add or subtract two rational expressions, we usually find a common denominator. We usually use the least common denominator (lcd) of the two quotients. To find this, we factor each denominator into primes and then form the produ

ct of the different prime factors, using the largest exponent that appears with each prime factor.

So say we have the denominators 24 and 18.

First, we factor these into 24=2^3*3 and 18=2*3^2 (*= multiplication)

To find the lcd, form product using largest exponent associated with each factor. So, lcd=2^3*3^2. Now don't forget to multiply with the numerator!!! (have to multiply 2^3 to the side with the 18, and 3^2 to the side with the 24)

In short, factor the bottom, find lcd, and then make every fraction have the denominator be equal to the lcd.

COMPLEX FRACTION: a quotient in which the numerator and/or denominator is a fractional expression. How do you do this? Well, first you solve the top half of the equation, and then the bottom half, and then multiply by reciprocal of the bottom! Nice little video on how to do it here, because I don't know how to explain the example in the book (fail)... so let's hope this video does a better job!!!

http://www.youtube.com/watch?v=HgIgZ5xbpiU

Rationalizing a denominator:

Again, pretty basic, something we've already learned. I'll

put an example down anyways though. On top of that, there is rationalizing a numerator, which is like rationalizing a denominator, except you are trying to get the numerator to equal one.

And then simplifying fractional expressions is just like complex fractions, so I don't feel the need to go through that same thing again! It's really basic, just simplify with common denominators and such!!!

I hope you find this section a breeze!!! :)

- Maggie Ridenour