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Question
Solve:
`2((2x - 1)/(x + 3)) - 3((x + 3)/(2x - 1)) = 5; x ≠ -3, (1)/(2)`
Solution
Given `2((2x - 1)/(x + 3)) - 3((x + 3)/(2x - 1)) = 5` ...(1)
Put `(2x - 1)/(x + 3) = y` in equation (1); we have
`2y - (3)/y = 5`
⇒ 2y2 – 5y – 3 = 0
⇒ 2y2 – 6y + y – 3 = 0
⇒ 2y(y – 3) + 1(y – 3) = 0
⇒ (y – 3)(2y + 1) = b
Either y – 3 = 0 or 2y + 1 = 0
⇒ y = 3 or y = `-1/2`
⇒ `(2x - 1)/(x + 3) = 3` or `(2x - 1)/(x + 3) = -1/2`
⇒ 2x – 1 = 3x + 9
or 2(2x – 1) = – (x + 3)
⇒ 3x – 2x = – 1 – 9
or 4x + x = 2 – 3
⇒ x = –10 or 5x = –1
i.e. `x = -1/5`
Thus, `x = -10, -1/5`
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