A few questions ... Any responses are appreciated...

[cr8zy4jj]

1. If 4 is substituted for x in the rational expression x-4 / x^2-16 , the result is 0/0. Mathematicians have been known to say "Any number divided by itself is 1." Does this mean that this expression is equal to 1 for x = 4? Explain why or why not.

2. 8x/x -2 - 2x-4/2-x - 8x/x-2 (those are 3 fractions that are to be subtracted and it said simplify if possible... I cant even begin to figure this one...

3. x^2+7x+10/x+5 Divided by x^2-4/5x-10 simplify if possible... *those are fractions also*

Thank you in advance....

 

[stapel]

1) This is asking for your thoughts. What are they? You've thought about "numbers" versus "expressions". Where are you stuck?

2) To learn how to add (and subtract) rational expressions, try here.

3) See (2). :wink:

 

[fasteddie65]

1. If 4 is substituted for x in the rational expression (x - 4)/(x^2 - 16) , the result is 0/0. Mathematicians have been known to say "Any number divided by itself is 1." Does this mean that this expression is equal to 1 for x = 4? Explain why or why not.

No, 0/0 is undefined. You can never divide by 0.

2. 8x/(x - 2) - (2x - 4)/(2 - x) - 8x/(x - 2) (those are 3 fractions that are to be subtracted and it said simplify if possible... I cant even begin to figure this one...

8x/(x - 2) - (2x - 4)/(2 - x) - 8x/(x - 2) = 8x/(x - 2) - (4 - 2x)/(x - 2) - 8x/(x - 2) =
[8x - (4 - 2x) - 8x]/(x - 2) = (2x - 4)/(x - 2) = 2(x - 2)/(x - 2) = 2 as long as x ? 2.


3. x^2+7x+10/x+5 Divided by x^2-4/5x-10 simplify if possible... *those are fractions also*

(x^2 + 7x + 10)/(x + 5) ÷ (x^2 - 4)/(5x - 10) = (x + 5)(x + 2)/(x + 5) ÷ (x + 2)(x - 2)/[5(x - 2)] = (x + 2) ÷ (x + 2)/5 = 5 as long as x ? -2.

Thank you in advance....