algrebra 2

can someone please help me im stumped on these two.

use analytical methods to solve the equation.

1+(1/x)=(42/x²)



(7/x-4)=1+(9/x+4)

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asked by tom
  1. 1 + 1/x = 42/x^2.

    Multiply both sides by x^2 and get:
    x^2 + x = 42,
    x^2 + x - 42 = 0,
    (x+7)(x-6) = 0.

    x+7 = 0,
    x = -7.

    x-6 = 0,
    x = 6.

    Solution Set: x=-7, and 6.


    7/(x-4) = 1 + 9/(x+4).

    7/(x-4) - 9/(x+4) = 1,
    LCM = (x-4)(x+4),
    (7(x+4) - 9(x-4)) / (x-4)(x+4) = 1,
    (7x+28-9x+36) / (x-4)(x+4) = 1,
    (-2x+64) / (x--4)(x+4) = 1,
    Cross Multiply:
    (x-4)(x+4) = -2x + 64,
    x^2 - 16 = -2x+64,
    x^2 + 2x - 80 = 0,
    (x-8)(x+10) = 0.

    x-8 = 0,
    x = 8.

    x+10 = 0,
    x = -10.

    Solution Set: x = 8, and -10.

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    posted by Henry

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