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Question
If `a/b = c/d`, prove that `(4a + 9b)/(4a - 9b) = (4c + 9d)/(4c - 9d)`.
Theorem
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Solution
`a/b = c/d`
Multiply the numerator by 4 and the denominator by 9 on both sides:
`(4a)/(9b) = (4c)/(9d)`
Apply Componendo and Dividendo,
`(4a + 9b)/(4a - 9b) = (4c + 9d)/(4c - 9d)`
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