Question 685591

Hi,

Please help me with this problem...

(1/x+8)+(1/x+5) = 1/2

Thank you in advance for your time and assistance...


I'm assuming it's {{{1/(x + 8) + 1/(x + 5) = 1/2}}}, as opposed to {{{(1/x) + 8 + (1/x) + 5 = 1/2}}}


Note that {{{x <> - 8}}}, or {{{x <> - 5}}}


Solving the former:
2(x + 5) + 2(x + 8) = (x + 8)(x + 5) ------- Multiplying by LCD, 2(x + 8)(x + 5)


{{{2x + 10 + 2x + 16 = x^2 + 13x + 40}}}


{{{4x + 26 = x^2 + 13x + 40}}}


{{{x^2 + 13x - 4x + 40 - 26 = 0}}}


{{{x^2 + 9x + 14 = 0}}}


(x + 7)(x + 2) = 0


{{{highlight_green(x = - 7)}}}   OR  {{{highlight_green(x = - 2)}}}


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