Why Do These Mathematical Expressions Seem Unequal?

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The discussion centers on a misunderstanding of mathematical expressions involving fractions. The user initially believes that the equation (x-4)(x+1) + (x+1)(x-4) should equal (x+1)(x-4), but finds a discrepancy when substituting a value for x. The confusion arises from not recognizing that when adding fractions, the denominators must be equal rather than summed. A clarification highlights that the correct approach is to keep the denominators the same while combining the numerators. Ultimately, the user acknowledges their mistake in applying the rules of fraction addition.
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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?
 
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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.
 
Slider,

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