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Question
Solve the following equation:
`1/("x - 1") + 2/("x" - 2) = 3/("x" - 3)`
Solution
`1/("x - 1") + 2/("x" - 2) = 3/("x" - 3)`
`= (1("x" - 2) + 2("x" - 1))/(("x" - 1)("x" - 2)) = 3/("x" - 3)`
`=> ("x" - 2 + 2"x" - 2)/("x"^2 - "2x" - "x" + 2) = 3/"x - 3"`
`=> (3"x" - 4)/("x"^2 - "3x" + 2) = 3/"x - 3"`
⇒ (x - 3)(3x - 4) = 3(x2 - 3x + 2)
⇒ 3x2 - 4x - 9x + 12 = 3x2 - 9x + 6
⇒ 3x2 - 13x - 3x2 + 9x = 6 - 12
⇒ - 4x = - 6
x = `(-6)/(-4) = 3/2 = 1 1/2`
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