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Question
If `(7"a" + 12"b")/(7"c" + 12"d")` then prove that `"a"/"b"="c"/"d"`
Solution
`(7"a" + 12"b")/(7"c" + 12"d") = (7"a" - 12"b")/(7"c" - 12"d")`
Applying alternendo,
`(7"a" + 12"b")/(7"a" - 12"b") = (7"c" + 12"d")/(7"c" - 12"d")`
Applying componendo and dividendo,
`(7"a" + 12"b" + 7"a" - 12 "b")/(7"a" + 12"b" - 7"a" + 12"b") = (7"c" + 12"d" + 7"c" - 12"d")/(7"c" + 12"d" - 7"c" + 12"d")`
`=> (14"a")/(24"b") = (14"c")/(24"d")`
Dividing both sides by `14/24`
`"a"/"b" = "c"/"d"`
Hence, proved.
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