Rational expressions, Mathematics

Now we have to look at rational expressions. A rational expression is a fraction wherein the numerator and/or the denominator are polynomials.  Here are some examples of rational expressions.

     6 /x -1          z 2  -1 /z 2 + 5      m4 + 18m + 1/ m2 - m - 6            4 x2 + 6 x -10/1

The last one might look a little strange as it is more commonly written 4 x2 + 6 x -10 . But, it's significant to note that polynomials may be thought of as rational expressions if we have to, although they hardly ever are.

There is an unspoken rule while dealing along with rational expressions which now we need to address. While dealing with numbers we know that division with zero is not allowed. Well the similar is true for rational expressions.  Thus, when dealing with rational expressions we will always suppose that whatever x is it won't give division by zero. Rarely do we write this limitation down, however we will always need to keep them in mind.

For the first one listed we have to ignore x = 1 .  The second rational expression is never being zero in the denominator and thus we don't have to worry regarding any restrictions.  Note down that the numerator of the second rational expression will be zero.  That is okay, we only need to ignore division by zero.  For the third rational expression we will have to avoid m = 3 and m =-2 .

The final rational expression shown above will never be zero in the denominator thus again we don't require having any restrictions.

The first topic which we have to discuss here is decreasing a rational expression to lowest terms. A rational expression has been decreased to lowest terms if all common factors from the numerator & denominator have been canceled out.  Already we know how to do this with number fractions so let's take a rapid look at an example. not reduced to lowest terms

                                               ⇒       1344_Rational Expressions.png    ⇐    reduced to lowest terms

 

 

 

 

With rational expression it works accurately the similar way.

not reduced to lowest terms ⇒ 496_Rational Expressions1.png

 

  1217_Rational Expressions2.png                               ⇐ reduced to lowest terms

However, we do need to be careful with canceling. There are little common mistakes that students frequently make with these problems.  Remind that to cancel a factor it has to multiply the whole numerator and the whole denominator.  Thus, the x+3 above could cancel as it multiplied the whole numerator & the whole denominator.  Though, the x's in the decreased form can't cancel as the x in the numerator is not times the whole numerator.

To see why the x's don't cancel out in the reduced form above put a number in & see what takes place. Let's plug in x=4.

Obviously the two aren't the similar number!

Thus, be careful with canceling out.  Since a general rule of thumb remember that you can't cancel out something if it's got a "+" or a "-" on one side of it. There is one exception of this rule "-" that we'll deal along with in an example later on down the road.

Posted Date: 4/6/2013 2:54:22 AM | Location : United States







Related Discussions:- Rational expressions, Assignment Help, Ask Question on Rational expressions, Get Answer, Expert's Help, Rational expressions Discussions

Write discussion on Rational expressions
Your posts are moderated
Related Questions

SQUARE 12 IN

Perform the denoted operation.                    (4/6x 2 )-(1/3x 5 )+(5/2x 3 ) Solution For this problem there are coefficients on each of term in the denominator thus

Factoring By Grouping It is a method that isn't utilized all that frequently, but while it can be used it can be somewhat useful. Factoring by grouping can be nice, however it

In the shape of a cone a tank of water is leaking water at a constant rate of 2 ft 3 /hour .  The base radius of the tank is equal to 5 ft and the height of the tank is 14 ft.

Solve the recurrence relation T (K) = 2T (K-1), T (0) = 1 Ans: The following equation can be written in the subsequent form:  t n - 2t n-1 =  0  Here now su

The larger of two supplementary angles exceeds the smaller by 180, find them. (Ans:990,810) Ans:    x + y = 180 0          x - y =  18 0        -----------------

First, larger the number (ignoring any minus signs) the steeper the line.  Thus, we can use the slope to tell us something regarding just how steep a line is. Next, if the slope

"To grow your brand, you need to encourage your existing customers to buy your product a liitle more often. It is far more important to maximise the number of times your buyers buy

Q. Multiplying Fractions Involving Negative Numbers? Ans. If you have only one negative sign, the result is still negative: If you have more than one, just remembe