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anonymous

  • one year ago

3/x+2 +2/x-2=8/(x+2)(x-2) Solve and tell if its extraneous

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  1. anonymous
    • one year ago
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    @Hero

  2. anonymous
    • one year ago
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    now you can have extraneous solutions because you have denominators

  3. anonymous
    • one year ago
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    :)

  4. anonymous
    • one year ago
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    \[\frac{x}{x+2}+\frac{2}{x-2}=\frac{8}{(x+2)(x-2)}\] you have a choice, you can either add on the left, or multiply both sides by \((x+2)(x-2)\) to clear the fractions

  5. anonymous
    • one year ago
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    multiply

  6. anonymous
    • one year ago
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    ok then the \((x+2)(x-2)\) cancels on the right leaving \(8\)

  7. anonymous
    • one year ago
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    on the left the first term will be \(x(x-2)\) and the second term will be \(2(x+2)\)

  8. anonymous
    • one year ago
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    by cancelling that leaves you with the equation \[x(x-2)+2(x+2)=8\] multiply out and solve the resulting quadratic

  9. anonymous
    • one year ago
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    x^2-2x+2x+4=8 x^2+4=8 x^2=4

  10. anonymous
    • one year ago
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    ok and if \(x^2=4\) then \(x=?\)

  11. anonymous
    • one year ago
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    x=+ or - 2

  12. anonymous
    • one year ago
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    right

  13. anonymous
    • one year ago
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    and in this case

  14. anonymous
    • one year ago
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    BOTH are extraneous, because both values would make the denominator equal to zero

  15. anonymous
    • one year ago
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    :) Thanks!

  16. anonymous
    • one year ago
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    yw

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