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Simplifying Rational Functions with Factoring and GCFs - Problem 2
This problem has two parts, I need to simplify the rational expression and I need to find any excluded values.
Well in order to simplify what I want to do is factor both at top and bottom and see if there’s any factors that I can cross out because they’d be the same at top and bottom. Well the top is a monomial it can’t be factored any further I’m just going to leave it as 18x to the third. But the bottom I can factor out the common factor of 6 that looks like this.
Now I can look for factors that are the same on top and bottom like 18 has the factors 6 and 3. 6 times 3 equals 18. So I can reduce this to 3/1 what I’m really looking at is 3x to the third on top on the bottom all I have is x plus 2.
Now a lot of students at this point attempted to cancel out of these X's with that x but you guys you got to remember you can only cancel out things if they are in multiplied form or if they are being factors.
On top I have factor if x right I have three times x times x times x, so x is a factor but in the bottom I have x plus 2; x isn’t being multiplied by anything that means I can’t cancel out those X's this is my most simplified form.
The second half of the problem it asked me to find any excluded values remember an excluded value is something that would make my expression undefined. It would be undefined if that denominator would be equals to 0. So in order to find my excluded values I’m going to set my denominator equal to 0 and solve for x.
I’ll have 6x is equal to -12; x is equal to -2 and that’s kind of tricky because this isn’t like the answer x minus 2 is not a solution meaning it makes this statement true or something. x minus 2 is what we are calling excluded value.
-2 is the value that makes this expression undefined because the denominator would equal 0. So again you guys just to summarize when you are asked to simplify rational expressions what you want to do is factor the top completely, factor the bottom completely cancel out anything that’s the same factor on top and bottom because it’s like 1 it’s like 3/3 is equal to 1.
Once that’s done go back and look for exclude values by setting your denominator equal to 0 one of the laws we have in Math is thou shall not divide by 0 because it's 0 when the bottom of the fraction is undefined.