prove that 1/1-x^m-n+1/1-x^n-m=1
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Answered by
10
L.H.S
1/[1-x^(m-n)] + 1/[1-x^(n-m)],
1/[1-x^m × x^(-n)] + 1/[1-x^n × x^(-m)],
x^n/(x^n - x^m) + x^m/(x^m - x^n),
x^n/(x^n - x^m) - x^m/(x^n - x^m),
now take the LCM here, we get
(x^n - x^m)/(x^n - x^m),
1
hence
L.H.S=R.H.S
Answered by
3
Step-by-step explanation:
According to the question,
We need to prove LHS = RHS
So,
LHS
now take the LCM here, we get
LHS= 1
and From the question,
RHS also equal to 1
LHS=RHS
Hence, this equation proved.
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