4/x+2 - 1/x+3 = 4/2x+1

Solve using factorization method.

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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] / [x2 + 5x + 6] = 4/(2x + 1)
⇒ [3x + 10] / [x2 + 5x + 6] = 4/(2x + 1)
⇒ 4x2 + 20x + 24 = 6x2 + 23x + 10
⇒ 2x2 + 3x - 14 = 0
⇒ (x - 2)(2x + 7) = 0
⇒ x = 2 or - 7/2

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