Mathematical geniuses. I need your help.?

Question

The following needs to be simplified. I have given up after 1 hour and 7 pages. i will write it out in words to make it easier to understand.

Simplifiy:
(a plus b over a minus b) minus (a minus b over a plus b)

Basically.
(a+b/a-b)-(a-b/a+b)
or
a+b______a-b
a-b ___-___a+b (ignore the lines)
I keep getting an answer of zero which is incorrect.

Answer 1

(a+b)/(a-b) - (a-b)/(a+b) = ...

the common denominator for both fractions is (a-b)(a+b)
=> multiply the first fraction (top and bottom) by (a+b) and the second one by (a-b)

= (a+b)·(a+b)/(a-b)·(a+b) - (a-b)·(a-b)/(a+b)·(a-b) =

= (a+b)² /(a-b)·(a+b) - (a-b)² /(a+b)·(a-b) =

= [ (a+b)² - (a-b)² ] /(a-b)·(a+b) =

= [ a² + 2ab + b² - (a² - 2ab + b²) ] /(a-b)·(a+b) =

4ab /(a-b)·(a+b)

(or 4ab /(a²-b²) )

Hope this helps.

Answer 2

I think you are not distributing correctly somewhere in your 7 pages.

You need to get the common denominator, which will be (a+b)(a-b) and that equals a^2-b^2.

Your first fraction is then (a+b)(a+b) / (a-b)(a+b) which equals (a^2+2ab+b^2) / (a^2-b^2).

Your second fraction is (a-b)(a-b) / (a-b)(a+b) which equals
(a^2-2ab+b^2)/(a^2-b^2).

Subtract them, and the numerators give
(a^2+2ab+b^2) - (a^2-2ab+b^2) = a^2 + 2ab + b^2 - a^2 + 2ab - b^2 = 4ab.

Therefore your answer will be 4ab / (a^2-b^2)

Answer 3

You are required to subtract two fractions

You need a common denominator (a+b)(a-b)

Multiply top and bottom of first fraction by a + b
Multiply top and bottom of second fraction by a - b

You will then have

(a+b)(a+b)/ (a+b)(a-b) minus (a-b)(a-b)/(a+b)(a-b)

numerator is (a^2 + 2ab + b^2) minus (a^2 - 2ab + b^2)
denominator is (a + b)(a - b)

numerator simplifies to 4ab so your answer is

4ab/[(a+b)(a-b)]

Answer 4

(a + b) / (a - b) - (a - b)/(a + b)

You need a common denominator of (a - b)(a + b)

So...
The first fraction becomes:
(a + b)(a + b) / (a - b)(a + b)
= (a^2 + 2ab + b^2) / (a - b)(a + b)

And the second one:
(a - b)(a - b) / (a - b)(a + b)
= (a^2 - 2ab + b^2) / (a - b)(a + b)

Now, you're subtracting those.... I'm just going to work on the numerators for a minute...

(a^2 + 2ab + b^2) - (a^2 - 2ab + b^2)
= a^2 + 2ab + b^2 - a^2 + 2ab - b^2
(Make sure you distribute that minus sign correctly!!!)
= 4ab

So, the final answer is

4ab / (a - b)(a + b)

Answer 5

First, please verify that the parentheses that I have inserted correctly describe the expression:
f = (a+b)/(a-b) - (a-b)/(a+b).
Multiply and divide through by (a+b)(a-b) to get:
((a+b)^2 - (a-b)*2)/((a+b)(a-b))
Expand the numerator and denominator:
(a*2 + 2ab + b*2 - a*2 + 2ab - b*2)/(a^2 - b^2)
Collect terms:
4ab/(a^2 - b*2). Done.

Answer 6

i imagine it relies upon on the way you outline "mathematical genius" it really is extra of a subjective definition. it really is extra objective to apply the time period "mathematically gifted" which sounds very very resembling the outline of this youngster. This youngster fairly seems to care about the that technique of the technological expertise in the back of mathematics and may want to invent some impressive issues in some unspecified time sooner or later. Sound like a really brilliant youngster! i might want to call him a math genius, why not?

Answer 7

I think you mean (a+b)/(a-b) - (a-b)/(a+b), in which case

[(a+b)(a+b)] / [(a-b)(a+b)] - [(a-b)(a-b)] / [(a+b)(a-b)] =

= [(a+b)^2 - (a-b)^2] / [(a-b)(a+b)]

= [a^2 + 2ab + b^2 - (a^2 - 2ab + b^2)] / [a^2 - ba + ab - b^2]

= (4ab) / (a^2 - b^2).

Answer 8

Call Me Pete is correct (dang, not fast enough!)

You could FOIL the bottom into what John, M, and Adam have, though. I think some of these people are changing their answers to be correct lol

Answer 9

(a+b/a-b) - (a-b/a+b) =
= (a+b)*2 - (a-b)*2 /(a-b)(a+b) =
= a*2+2ab+b*2-a*2+2ab-b*2/(a-b)(a+b)
= 4ab/(a-b)(a+b)

*2 means exponent

Answer 10

(a+b/a-b) - (a-b/a+b)
= [(a+b)^2/(a-b)(a+b)] - [(a-b)^2/(a+b)(a-b)]
= [(a+b)^2 - (a-b)^2] / (a+b)(a-b)
= [a^2 + 2ab + b^2 - a^2 + 2ab - b^2] / (a+b)(a-b)
= 4ab / (a^2 - b^2)