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Question
Write the following in the simplest form:
(b-2 - a-2) ÷ (b-1 - a-1)
Solution
(b-2 - a-2) ÷ (b-1 - a-1)
This can be written as,
= `(1/b^2 - 1/a^2)/(1/b - 1/a)`
= `{(1/b)^2 - (1/a)^2}/(1/b - 1/a)`
= `= {(1/b + 1/a) (1/b - 1/a)}/(1/b — 1/a)`
We get,
= `1/b + 1/a`
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