Question

simplify :


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maths question​

Answer 1

Qᴜᴇsᴛɪᴏɴ:-

1/[1 + (x)^b-a + (x)^c-a] + 1/[1 + (x)^a-b + (x)^c-b] + 1/[1 + (x)^a-c + (x)^b-c]

Aɴsᴡᴇʀ:-

First solving 1/[1 + (x)^b-a + (x)^c-a] :-

We know p^(m-n) = (p^m)/(p^n)

p^m * p^n = p^(m+n)

1/[1 + (x)^b-a + (x)^c-a]

=> 1/[1 + x^b/x^a + x^c/x^a]

=> 1/[ (x^a + x^b + x^c)/x^a]

=> x^a/(x^a + x^b + x^c)

Solving 1/[1 + (x)^a-b + (x)^c-b] :-

1/[1 + (x)^a-b + (x)^c-b]

=> 1/[( + x^a/x^b + x^c/x^b]

=> 1/[(x^b + x^a + x^c)/x ^b]

=> x^b/(x^b + x^a + x^c)

Solving 1/[1 + (x)^a-c + (x)^b-c] :-

1/[1 + (x)^a-c + (x)^b-c]

=> 1/[1 + x^a/x^c + x^b/x^c]

=> 1/[(x^c + x^a + x^b)/x^c]

=> x^c/(x^c + x^a + x^b)

Adding them :-

x^a/(x^a + x^b + x^c) + x^b/(x^b + x^a + x^c) + x^c/(x^c + x^a + x^b)

=> x^a/(x^a + x^b + x^c) + x^b/(x^a + x^b + x^c) + x^c/(x^a + x^b + x^c )

=> (x^a + x^b + x^c)/(x^a + x^b + x^c)

=> 1

Ans. = 1