Thread: abstract algebra!

I really need help with this question..

Which of the following are true for all real numbers a,b>0? For those that are not always true, give specific values of a,b>0 where they fail

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

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

(c) 1/a +1/b = (a+b)/ab

I like c)

If you can't do this question, you will have some trouble in an algebra course. Do you know how to add fractions?

I have very little maths back ground. I need an example to be able to understand

You need to make a common denominator, try

thanks, but i do understand that, What im confused is how does that relate wiht this question.

would u please be able to demonstrate on (a), (b) and/or (c)
thank you

Originally Posted by tim_mannire

thanks, but i do understand that, What im confused is how does that relate wiht this question.

would u please be able to demonstrate on (a), (b) and/or (c)
thank you

I have demonstrated c) as it is able to be proved, the others can't be.

Job done.

Great, I finally understand.

But for where it says "For those that are not always true, give specific values of a,b>0 where they fail." how can i do that ?

also, what about fractions like these?

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


a/(a+b) = 1/b


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

To show that a statement doesn't hold, all you need to do is find a counterexample to what the statement asserts. For instance if you want to disprove

,

you can just notice that

.

Just try a couple of values and you'll soon find a pair which violates the assertion.