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Question
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
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Solution
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
⇒ `(4(x + 3) - 1(x + 2))/((x + 2)(x + 3)) = 4/(2x + 1)`
⇒ `(4x + 12 - x - 2)/(x^2 + 2x + 3x + 6) = 4/(2x + 1)`
⇒ `(3x + 10)/(x^2 + 5x + 6) = 4/(2x + 1)`
⇒ (3x + 10)(2x + 1) = 4(x2 + 5x + 6)
⇒ 6x2 + 3x + 20x + 10 = 4x2 + 20x + 24
⇒ 2x2 + 3x – 14 = 0
⇒ 2x2 + 7x – 4x – 14 = 0
⇒ 2x2 + 7x – 4x – 14 = 0
⇒ x(2x + 7) – 2(2x + 7) = 0
⇒ (2x + 7)(x – 2) = 0
If 2x + 7 = 0 or x – 2 = 0
Then x = `(-7)/2` or x = 2
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