Questions on Algebra: Expressions involving variables, substitution answered by real tutors!

Algebra ->  Algebra  -> Expressions-with-variables -> Questions on Algebra: Expressions involving variables, substitution answered by real tutors!     (Log On)
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!

   

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.: 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.
Answer by Fombitz(1756) 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.
(x^2 - 9)/(x^2 + 3x)
You can factor the top term,
x^2-9=(x+3)(x-3)
and also the bottom one,
x^2+3x=x(x+3)
(x^2 - 9)/(x^2 + 3x)=((x+3)(x-3))/(x(x+3))
(x^2 - 9)/(x^2 + 3x)=(cross(x+3)(x-3))/(x*cross((x+3)))
(x^2 - 9)/(x^2 + 3x)=(x-3)/x
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.: 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.
Answer by stanbon(19020) 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.