1. 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

2. I like c)

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

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

5. $\displaystyle \frac{1}{a}+\frac{1}{b}$

You need to make a common denominator, try $\displaystyle a \times b = ab$

$\displaystyle = \frac{1}{a} {\color{red}\times 1}+\frac{1}{b} {\color{red}\times 1}$

$\displaystyle = \frac{1}{a} {\color{red}\times \frac{b}{b}}+\frac{1}{b} {\color{red}\times \frac{a}{a}}$

$\displaystyle = \frac{b}{ab} +\frac{a}{ab}$

$\displaystyle = \frac{b+a}{ab}$

$\displaystyle = \frac{a+b}{ab}$

6. 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

7. 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.

8. 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 ?

9. also, what about fractions like these?

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

a/(a+b) = 1/b

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

10. 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

$\displaystyle \frac{1}{a}+\frac{1}{b} = \frac{1}{a+b}$,

you can just notice that

$\displaystyle \frac{1}{1}+\frac{1}{1} \not = \frac{1}{1+1}$.

Just try a couple of values and you'll soon find a pair which violates the assertion.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}