1. ## Simple algebraic sum

I have this algebraic fraction sum I need help with.
Code:
x^2 - 7x
-------
x^2 - 49
I worked it out by cancelling out the x^2 on both sides, and then simplifing the rest, and my answer was:

Code:
x
--
7
I read that the correct method would be this:
Code:
   x(x-7)            x
---------      =   ----
(x+7)(x-7)          x-7
Why is this right, and my method wrong? My reasoning is that the denominators are the same for x^2 and 7x, so I can just work by simplifying them...

2. Hey,

there is a formula a^2 - b^2 = (a+b)*(a-b). You have to use this formula on your denominator.

Liptak

3. Yep thats factorising for difference of squares. I want to know why use that when I can just simplify the sum the way I did.

4. You can't cancel out the x^2 on both sides, beacause there is a minus sign between the elements. You could do it if there was a multiplication only...

5. $\displaystyle \frac{7- 5}{7- 2}= \frac{2}{5}$ NOT $\displaystyle \frac{-5}{-2}= \frac{5}{2}$. You can cancel like terms when they are multiplied by the rest of the numerator or denominator, not when they are added to them.

6. Originally Posted by yorkey
Code:
   x(x-7)            x
---------      =   ----
(x+7)(x-7)          x-7
Should be x / (x + 7).

Let (as example) x = 8 and see what happens your way...