Algebra 1 Finding Common Denominators of Polynomial Fractions
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How Common
Finding Common Denominators of Polynomial Fractions

 
 In the last few pages, we have been working with things called equations.
 
 Oh yeah? What's an equation?
 
 AN EQUATION IS SOMETHING WHERE YOU HAVE 
 AN EQUAL SIGN BETWEEN TWO GROUPS OF STUFF
 
 That is ...

STUFF = STUFF

 
 Like:

4X + 5 = 12

 
 If we just have some terms and no equal sign
 THAT is called an EXPRESSION.
 
 Expression - equation - what's the difference?
 
 PLENTY!
 
 When we have an EQUATION
 we can do almost anything we want to it to solve it.
 We just have to do the same thing to both sides of the equation.
 
 When we have an expression, we don't have two sides.
 We just have one thing.
 We can't do anything that would change the value of the expression.
 That means all we can do is multiply it by 1 or add 0.
 
 That doesn't sound like very much.
 

 No it isn't. But using some tricks, it's often enough.

 
 Old Time Review:
 
 What would you do if you had:
 

 
 We would find a common denominator and subtract.
 
 There are lots of ways to find a common denominator.
 
 The easiest way is to just call it the product
 of the two denominators.
 
 The denominators are 3 and 7, so the common denominator
 is 3 x 7 = 21.
 
 Since this is an expression, not an equation
 we can only multiply it by one or add zero.
 
 Here we will multiply the first term by 7/7 
 and multiply the second term by 3/3 ...
 

 
 That gives us our common denominator,
 and we can subtract.
 
 NOW BACK TO ALGEBRA
 
 Say we have this ...
 

 

 
 We need to do the same process.
 
 The easiest common denominator is (X - 3)(X + 3).
 
 Multiply each term by the name for 1
 that gets us a common denominator
 subtract and simplify ...
 

 

 
 Did you catch the signs on the subtraction?
 
 Now simplify ...

 

 
 If we had a problem that used addition instead of subtraction
 it would work the same way ...
 

 
 OK. Let's try another one ...
 

 
 so at first, this one is a problem. 
 The term on the right is just an X.
 
 The deal is, we can put a denominator of 1
 under anything so ...

 so:

 
 The common denominator is 4 1 = 4.
 The term on the left already has this denominator,
 so we just need to multiply the term on the right by 4/4.
 
 Then we can add and simplify ...
 

 
 There's nothing special about X.
 It's just the variable we tend to use.
 
 Try this ...
 

 
 The first step is to find a common denominator.
 
 The first term denominator is Ho.
 The second term denominator is Hi.
 That makes the common denominator Hi x Ho.
 Math people might write this as Hi Ho.
 The first term denominator needs Hi.
 The second term denominator needs Ho.
 We don't have an equation, 
 so we can only multiply terms by another name for 1.
 The first term gets multiplied by Hi/Hi.
 The second term gets multiplied by Ho/Ho.
 We get ...
 

 

 
 Now it's time for a math joke ...
 
 Can you factor a worm out of an apple?
 
 Sure you can.
 
 You want to start with 

Apple

 

 And end up with ...

 Apple = Worm SOMETHING

 
 Whatever that something is,
 when you multiply it times Worm you get apple.
 Can you figure out what it is???
 

 

   copyright 2005 Bruce Kirkpatrick

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