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Question
If b = `(2"a")/("a" - 2)`, and c = `(4"b" - 3)/(3"b" + 4)`, then express c in terms of a.
Solution
Given b = `(2"a")/("a" - 2), and "c" = (4"b" - 3)/(3"b" + 4)`
Substituting b = `(2"a")/("a" - 2) "in c" = (4"b" - 3)/(3"b" + 4)`
c = `(4((2"a")/("a" - 2)) - 3)/(3((2"a")/("a" - 2)) + 4)`
⇒ c = `((8"a")/("a" - 2) - 3)/((6"a")/("a"- 2) + 4`
⇒ c = `((8"a" - 3("a" - 2))/("a" - 2))/((6"a" + 4("a" - 2))/("a" - 2)`
⇒ c = `(8"a" - 3("a" - 2))/(6"a" + 4("a"- 2)`
⇒ c = `(8"a" - 3"a" + 6)/(6"a" + 4"a" - 8)`
⇒ c = `(5"a" + 6)/(10"a" - 8)`.
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