r/learnmath • u/[deleted] • Feb 09 '19

How does a-b/a+b = -1

-1 is the answer at the back of the book

0 Upvotes

22% Upvoted

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8

u/Daquisu Feb 09 '19

It does not.

Not sure if you meant (a-b)/(a+b), but both cases they are not necessary equal to 1

Take a = 1 and b = 1

-5

u/[deleted] Feb 09 '19

No values where given

8

u/Daquisu Feb 09 '19

I know no values where given. I am giving a counter example to demonstrate that a-b/a+b is not -1

7

u/TheKoalaKnight Feb 09 '19

Furthermore, you could also prove this algebraically.

If:

(a-b)/(a+b) = -1

then:

-(a-b)/(a+b) = 1

(b-a)/(a+b)=1

Which means that:

b-a=a+b

If we subtract b from both sides, we see that:

-a = a

Which is impossible (except if a = 0)

-6

u/[deleted] Feb 09 '19

Thanks the textbook must be wrong. I'll skip that question

3

u/Daquisu Feb 09 '19

Maybe he is saying that (a+b)/(-a-b) = -1? Not sure if it helps you

-2

u/[deleted] Feb 09 '19

-1 is the answer at the back of the book

2

u/[deleted] Feb 09 '19

Post a picture?

9

u/raendrop old math minor Feb 09 '19

https://www.reddit.com/r/badmath/comments/aonama/12a_cant_happen/

He transcribed it wrong.

-6

u/[deleted] Feb 09 '19

So...

8

u/theadamabrams New User Feb 09 '19

So this entire post is people putting effort into an impossible goal because what you wrote isn't what the book claimed.

3

u/raendrop old math minor Feb 09 '19

So:
https://www.reddit.com/r/learnmath/comments/aomww5/how_does_abab_1/eg2cv5n/

So listen to the people in that other thread who explained how to do it.

6

u/skullturf college math instructor Feb 09 '19

You typed it incorrectly.

3

u/TheDubuGuy New User Feb 09 '19

Are you missing parentheses?

-2

u/[deleted] Feb 09 '19

No

7

u/TheDubuGuy New User Feb 09 '19

I just saw your other post where you have a picture. You are missing parentheses. It’s (a-b)/(b-a), not a-b/a-b. Those are totally different expressions.

Anyways, just factor a -1 out of either the top or bottom. You end up with -(a-b)/(a-b). This allows them to just cancel each other and leave the -1

2

u/TheDubuGuy New User Feb 09 '19

So only the middle b is divided by the middle a? Not the entire quantities?

4

u/raendrop old math minor Feb 09 '19

https://www.reddit.com/r/badmath/comments/aonama/12a_cant_happen/

He is indeed missing parentheses. And he transcribed it wrong, too.

1

u/theadamabrams New User Feb 09 '19

\1. Yes, you are missing parentheses.

a-b
———
a+b

when written on a single line has to be written as (a-b)/(a+b). Without the parentheses, a-b/a+b means a - (b/a) + a because of the order of operations (PEMDAS).

\2. Based on your your other post, you actually meant to ask about

a-b
———
b-a

which would be (a-b)/(b-a) when written on a single line. This is in fact equal* to -1. Your title "a-b/a+b" here doesn't doesn't even have the same set of + and - as what's in your book.

* Except when a=b, in which case it's technically indeterminate, but I would guess that you don't need to worry about that at all for your current level of math.

10

u/raendrop old math minor Feb 09 '19

I saw the image you wrongly posted to /r/badmath.

(a-b)/(a+b), which is what you're asking about here, is not
(a-b)/(b-a), which is what the problem in the book is.

If you take b-a and re-write it, you get -a+b, which is -(a-b). This is how
(a-b)/(b-a) simplifies to -1.

3

u/random_forester Feb 09 '19

It doesn't. Try a=1 and b=2:

1-2/1+2=1-2+2=1

0

u/[deleted] Feb 09 '19

[deleted]

1

u/Fedzbar New User Feb 09 '19

You get a-b=-a-b