Question

If (u,v) = u + v/u + v, find F(1/u, 1/v) + F(u, v).

Answer 1

$$
\text{if } \ \ f(u,v) = \cfrac{u+v}{u+v}\\
\text{find}\\
f\pmatrix{\frac{1}{u}, \frac{1}{v}}+f(u,v) \huge ?
$$

Answer 2

Yes.

Answer 3

hmmm, are just expecting the expand, because is quite unnecessary :/

Answer 4

a/a = 1
so
same/same =1

and \(\cfrac{u+v}{u+v} = 1\)

Answer 5

the 2nd function with the reciprocals, simple make the variables a fraction, but you'd still remain with \(\large \frac{same}{same} \)

Answer 6

$$
\text{if } \ \ f(u,v) = \cfrac{u+v}{u+v} = 1\\
\text{then}\\
f\pmatrix{\frac{1}{u},\frac{1}{v}} =
\cfrac{
\frac{1}{u}+\frac{1}{v}
}{
\frac{1}{u}+\frac{1}{v}
} = 1
$$

Answer 7

Oops, there has been a mistake. f(u, v) = u+v/u-v

sorry :)

Answer 8

using slope?

Answer 9

\[f \left( u,v \right)=\frac{ u+v }{ u-v }\]
\[f \left( \frac{ 1 }{ u },\frac{ 1 }{ v } \right)=\frac{ \frac{ 1 }{u }+\frac{ 1 }{ v } }{\frac{ 1 }{ u }-\frac{ 1 }{ v } }\]
\[=\frac{ \frac{ v+u }{uv } }{ \frac{ v-u }{ uv } }\]
\[=\frac{ v+u }{uv}*\frac{ uv }{ v-u }\]
\[=-\frac{ u+v }{u-v }=-f \left( u,v \right)\]
\[Hence f(u,v)+f \left( \frac{ 1 }{u },\frac{ 1 }{ v } \right)=0\]

Answer 10

The exact question is:
If (u, v)= u+v/u-v, find F(1/u, 1/v) + F(u, v).

Answer 11

see surjithayer's line above :)

Answer 12

@raechelvictoria look at all the effort that could have been saved if you typed the problem accurately in the first place, or looked carefully when jdoe0001 asked you if the typeset version was correct?

Answer 13

Yep, he's got the right idea.

Answer 14

Be as careful as you want us to be in helping you :-)

Answer 15

@whpalmer4 @jdoe0001 I'm really really sorry :(((((((( thank you for your efforts in answering my question :)

Answer 16

yw