Why Do These Mathematical Expressions Seem Unequal?

[Holocene]

In order to see the problem here, you need to refer to following link:

http://img.photobucket.com/albums/v224/TurbineSpeed/Picture402887.jpg

I understand how they got the expression in the numerator. What I cannot figure out is how they got the denominator.

By their math, (x-4)(x+1) + (x+1)(x-4) = (x+1)(x-4)

This does not seem correct. Give a value to x such as x = 6, and:

(2)(7) + (7)(2) = 14 + 14 = 28

Now if we apply this value to the right member, we get:

(7)(2) = 14.

14 is NOT equal to 28.

What am I doing wrong?

 

[slider142]

Holocene,
a/b + c/b = (a+c)/b
As an example, if you have an eighth of a pizza and have another (one-eighth sized) slice of pizza, you have eaten 2/8=1/4 of the pizza, not 2/16 = 1/8.

 

[Holocene]

Slider,

Thank you, but how can (x-4)(x+1) + (x+1)(x-4) be equal to (x+1)(x-4)?

 

[Holocene]

WOW! Apparently I had forgotten that when you add fractions you do NOT add the denominators together. Instead, they must simply be equal. Man, I feel stupid for being tripped up over this one.

Slider, thanks, I can't believe I forgot this simple rule.