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23 February, 21:01

Solve the rational equation 1 / (x-2) - 1 / (x+3) = 1/5

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  1. 23 February, 22:46
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    x = 5.09, - 6.09.

    Step-by-step explanation:

    1 / (x-2) - 1 / (x+3) = 1/5

    Multiply through by the LCM 5 (x-2) (x+3):

    5 (x + 3) - 5 (x - 2) = (x - 2) (x + 3)

    5x + 15 - 5x + 10 = x^2 + x - 6

    x^2 + x - 31 = 0

    x = [ - 1 + / - sqrt (1 - 1*1*31) ] / 2

    x = 5.09, - 6.09.
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