SOLUTION: Please help me solve the following problem: Simplify the expression (x^2 - 9)/(x^2 + 3x) My attempt to this problem was to cancel out the x^2 because they divided each other,

Algebra ->  Expressions-with-variables -> SOLUTION: Please help me solve the following problem: Simplify the expression (x^2 - 9)/(x^2 + 3x) My attempt to this problem was to cancel out the x^2 because they divided each other,       Log On


   

Question 153544: Please help me solve the following problem:
Simplify the expression (x^2 - 9)/(x^2 + 3x)
My attempt to this problem was to cancel out the x^2 because they divided each other, and then i simplified -9/3x to -3x. But when i check to see if my work is correct by substituting x for 2, the answers did not match.
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the expression in the parentheses is a unique expression.
You can only divide or cancel out terms, inside parentheses, if they match exactly.
%28x%5E2+-+9%29%2F%28x%5E2+%2B+3x%29
You can factor the top term,
x%5E2-9=%28x%2B3%29%28x-3%29
and also the bottom one,
x%5E2%2B3x=x%28x%2B3%29
%28x%5E2+-+9%29%2F%28x%5E2+%2B+3x%29=%28%28x%2B3%29%28x-3%29%29%2F%28x%28x%2B3%29%29

%28x%5E2+-+9%29%2F%28x%5E2+%2B+3x%29=%28x-3%29%2Fx

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify the expression (x^2 - 9)/(x^2 + 3x)
My attempt to this problem was to cancel out the x^2 because they divided each other, and then i simplified -9/3x to -3x. But when i check to see if my work is correct by substituting x for 2, the answers did not match.
---------------
You may only cancel "factors" that are common to the numerator and to the
denominator.
x^2 is a "term" in the numerator and a "term" in the denominator and
may not be cancelled.
Example (2 + 3)/(2 + 5)
If you cancelled the "2" you would get 3/5; but the answer should be 5/7.
Don't cancel terms.
------------------------
Simplify the expression (x^2 - 9)/(x^2 + 3x)
Factor where you can to get:
[(x-3)(x+3)] / [x(x + 3)]
Notice that the (x+3) is a factor of the numberator and of the denominator
so you may cancel it to get:
= (x-3)/(x)
Notice that you cannot cancel the "x" because it is a "term" and not a factor in the numerator.
===============
Cheers,
Stan H.