math problem: solve for u?

( -2/(5u+10) ) -1 = 2/ (u+2)

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  • 1 decade ago
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    Express 1 as a fraction:

    ( -2/(5u+10) ) - (5u+10)/(5u+10) = 2/ (u+2)

    Subtract fractions on left side:

    (-2-5u-10)/(5u+10) = 2/(u+2)

    Cross multiply the denominators:

    (u+2)(-2-5u-10) = 2(5u+10)

    Multiply out:

    -2u-5u²-10u-4-10u-20 = 10u+20

    Combine terms:

    5u²+32u+44 = 0.

    Using the quadratic formula, we get

    u = -32/(5)(2) ± (√[32²-(4)(5)(44))/(5)(2); or

    u = -3.2 ± 1.2, or u = -4.4 and -2.

    But, we see u = -2 is not allowed, as it will result in division by zero in both denominators of the original equation. So the only answer is

    u = -4.4.

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