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Question
Solve the following equations for the unknown: `2 + (3x - 2)/(3x + 2) = (3x + 2)/(x + 1)`
Solution
`2 + (3x - 2)/(3x + 2) = (3x + 2)/(x + 1)`
⇒ 2 = `(3x + 2)/(x + 1) - (3x - 2)/(3x + 2)`
⇒ 2 = `((3x + 2)(3x + 2) - (3x - 2)(x + 1))/((x + 1)(3x + 2)`
⇒ 2(x + 1)(3x + 2) = (3x + 2)(3x + 2) - (3x - 2)(x + 1)
⇒ 2[3x2 + 2x + 3x + 2] = [9x2 + 6x + 6x + 4] - [3x2 + 3x - 2x - 2]
⇒ 6x2 + 4x + 6x + 4 = 9x2 + 6x + 6x + 4 - 3x2 - 3x + 2x + 2
⇒ 4x = 6x - 3x + 2x + 2
⇒ -x = 2
⇒ x = -2.
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