SOLUTION: How do you check your answer after simplifying a rational expression? For example, I took {{{(4x^2- 12x + 9)/(10x^2 - 11x - 6) }}} and simplified it to {{{(2x-3)/(5x+2)}}}. Ho

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you check your answer after simplifying a rational expression? For example, I took {{{(4x^2- 12x + 9)/(10x^2 - 11x - 6) }}} and simplified it to {{{(2x-3)/(5x+2)}}}. Ho      Log On


   

Question 162632: How do you check your answer after simplifying a rational expression?
For example,
I took %284x%5E2-+12x+%2B+9%29%2F%2810x%5E2+-+11x+-+6%29+ and simplified it to
%282x-3%29%2F%285x%2B2%29. However, the directions also want the answer to be checked but the book I give an example on how to check such a complex problem. I f you can show me how to go about checking the answer for this problem it would be helpful.
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

Substitute a number for x in the original expression
and then substitute it in the final answer and see if 
you get the same result.

First substitute x=0 in the original problem:

%284x%5E2-+12x+%2B+9%29%2F%2810x%5E2+-+11x+-+6%29+
%284%280%29%5E2-+12%280%29+%2B+9%29%2F%2810%280%29%5E2+-+11%280%29+-+6%29+
%280-0%2B9%29%2F%280-0-6%29
9%2F%28-6%29
-3%2F2

You could have done that in your head!

Now substitute x=0 in your final answer:

%282%280%29-3%29%2F%285%280%29%2B2%29
%280-3%29%2F%280%2B2%29
%28-3%29%2F2
-3%2F2

They're the same!  Both -3%2F2!
You could have done that in your head, too.
That's not a perfect check, but it is good
evidence that it is correct.  [However, if 
you hadn't have gotten the same result you 
would have known for certain that your
answer would have been wrong!]

To be much surer, also substitute x=1 
in the original expression and also in the 
final answer. 

Substitute x=1 in the original problem:

%284x%5E2-+12x+%2B+9%29%2F%2810x%5E2+-+11x+-+6%29+
%284%281%29%5E2-+12%281%29+%2B+9%29%2F%2810%281%29%5E2+-+11%281%29+-+6%29+
%284%2A1-12%2B9%29%2F%2810%2A1-11-6%29
%284-12%2B9%29%2F%2810-11-6%29
%281%29%2F%28-7%29
-1%2F7

Now substitute x=1 in your final answer:

%282%281%29-3%29%2F%285%281%29%2B2%29
%282-3%29%2F%285%2B2%29
%28-1%29%2F7
-1%2F7

They're the same!  Both -1%2F7!

When both x=1 and x=0 give the same results when
substituted in the original and in the final answer,
then it is extremely likely that your answer is 
correct.  You can also substitute x=2 or any 
other number you choose if you want to be absolutely 
sure!

Edwin