SOLUTION: 1) If a is a rational number, is it always, sometimes, or never true that a^2-3a over a-3 =a? Explain. Please help me! I have no idea what I am doing. lol

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1) If a is a rational number, is it always, sometimes, or never true that a^2-3a over a-3 =a? Explain. Please help me! I have no idea what I am doing. lol      Log On


   

Question 199243: 1) If a is a rational number, is it always, sometimes, or never true that a^2-3a over a-3 =a? Explain.
Please help me! I have no idea what I am doing. lol
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E2-3a%29%2F%28a-3%29 Start with the given expression.


%28a%28a-3%29%29%2F%28a-3%29 Factor the numerator


%28a%2Ahighlight%28%28a-3%29%29%29%2Fhighlight%28%28a-3%29%29 Highlight the common terms.


%28a%2Across%28%28a-3%29%29%29%2Fcross%28%28a-3%29%29 Cancel out the common terms.


a Simplify


So %28a%5E2-3a%29%2F%28a-3%29=a where a%3C%3E3. So the statement is always true.


Note: "a" can be any complex number (it doesn't have to be rational)