Question

If a,b, c are real numbers such that (ab)/(a + b) = 1/3, (bc)/(b + c) = 1/4 , (ca)/(c + a) = 1/5 the value of abc/ab + bc + ca is​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• $\frac{abc}{ab+bc+ca} = \frac{1}{6}$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

☆ɢɪᴠᴇɴ☆

• $\frac{ab}{a+b} = \frac{1}{3}$

• $\frac{bc}{b+c} = \frac{1}{4}$

• $\frac{ca}{c+a} = \frac{1}{5}$

☆ᴛᴏ ғɪɴᴅ☆

• $\frac{abc}{ab+bc+ca}$

☆ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ☆

Here,

$\frac{ab}{a+b} = \frac{1}{3}\to \frac{a+b}{ab}= 3$

$\frac{bc}{b+c} = \frac{1}{4}\to \frac{b+c}{bc} = 4</p><p>$

$\frac{ca}{c+a} = \frac{1}{5}\to \frac{c+a}{ca} = 5</p><p>$

Now,

$\: \: \: \frac{abc}{ab + bc + ca} = \frac{2abc}{2ab + 2bc + 2ca}$

$=\frac{2}{ \frac{2ab + 2bc + 2ca}{abc} } = \frac{2}{ \frac{ab + bc + bc + ca + ca + ab}{abc} }$

$= \frac{2}{ \frac{ab + bc}{abc} + \frac{bc + ca}{abc} + \frac{ca + ab}{abc} }$

$= \frac{2}{ \frac{b(c + a)}{abc} + \frac{c(a + b)}{abc} + \frac{a(b + c)}{abc}}$

$= \frac{2}{ \frac{c + a}{ca} + \frac{a + b}{ab} + \frac{b + c}{bc}}$

$= \frac{2}{5+ 3 + 4}$

$= \frac{2}{12}$

$= \frac{1}{6}$

Answer 2

Answer:

1/6 is the answer