Sum of fractions with reciprocal powers of a base: multiply through by a power

This type of question, asked 2 times: CDS 1 2018, CDS 1 2020. All 2 questions below, oldest first.

Try each one first, then open its answer.

Question 1
CDS 1 2018
19 $\frac{1}{1 + x^{b-a} + x^{c-a}} + \frac{1}{1 + x^{a-b} + x^{c-b}} + \frac{1}{1 + x^{a-c} + x^{b-c}}$
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Question 2
CDS 1 2020
19 $\frac{1}{a^{m-n} - 1} + \frac{1}{a^{n-m} - 1}$
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