Simplifying algebraic fractions x in numerator and denom.

[Svetlana_Vein]

Homework Statement

(x+3)(x-2)/x²-2x

Homework Equations

The Attempt at a Solution

(x+3)(x-2)/x(x-2) = (x+3)/x

What I don't understand is why I can't simplify this further for instance the x's cancel to give 1:

(1+3)/1 = 4/1 = 4

Is it because there is no x next to the 3?

Many thanks :)[/B]

 

[DaveE]

yes. For example, what if x = 3, then (x+3)/x = 2

 

[Svetlana_Vein]

yes. For example, what if x = 3, then (x+3)/x = 2

Thanks for clarifying Dave.

 

[Mark44]

Homework Statement

(x+3)(x-2)/x²-2x

You need two more parentheses -- like so:
(x+3)(x-2)/(x²-2x)

Homework Equations

The Attempt at a Solution

(x+3)(x-2)/x(x-2) = (x+3)/x

And here:
(x+3)(x-2)/(x²-2x) = (x + 3)/x

What I don't understand is why I can't simplify this further for instance the x's cancel to give 1:

(1+3)/1 = 4/1 = 4

Is it because there is no x next to the 3?

No, the x's don't cancel. Cancellation can happen only when you have the same factors in numerator and denominator. In your final expression, x and 3 are not factors (not multiplied). They are terms -- expressions that are added or subtracted.
Examples:
$\frac {2 \cdot 5} 5 = \frac 2 1$ -- We can cancel the 5's, since 5 is a factor in both the numerator and denominator (you can think of the other factor in the denominator as being 1).

$\frac {2 + 5} 5 = \frac 7 5 \ne 2$
The latter number would be the result if you canceled the 5's. Obviously this is incorrect, since 5 is not a factor in the numerator.