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Question
Solve for x :
`1/(2x - 3) + 1/(x - 5) = 1 1/9 , X != 3/2, 5`
Solution
We have
`1/(2x - 3) + 1/(x - 5) = 1 1/9`
`=> (x - 5 + 2x - 3)/((3x - 3)(x - 5)) = 10/9`
`=> (3x - 8)/(2x^2 - 13x + 15) = 10/9`
⇒9(3x − 8) = 10(2x2 − 13x + 15)
⇒27x − 72 = 20x2 − 130x + 150
⇒20x2 − 157x + 222 = 0
⇒20x2 − 120x − 37x + 222 = 0
⇒20x(x − 6) − 37(x − 6) = 0
⇒(20x − 37)(x − 6) = 0
`=> x = 37/20 , 6`
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