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anonymous

  • 5 years ago

What are the real and extraneous solutions in this equation: (x)/(x+2) + (5)/(x-3) = (25)/(x^2-x-6)

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  1. radar
    • 5 years ago
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    Roots are x=-5, x=3, the x=3 is an extraneous root.

  2. anonymous
    • 5 years ago
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    ok thanks. could you show me how you found those answers?

  3. radar
    • 5 years ago
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    Yes be glad to. First I did the addition. The common denominator is (x+2)(x-3)

  4. radar
    • 5 years ago
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    The numerators are then x(x-3) +5(x+2) over the common denominator of (x+2)(x-3) kind of like this: x(x-3) +5(x+2) -------------- =25/(x^2-x-6) (x+2)(x-3) You follow so far?

  5. anonymous
    • 5 years ago
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    yes i do.

  6. radar
    • 5 years ago
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    Now lets work on the denominator of the fraction on the right side of the equal sign. the denominator is x^2-x-6 This can be factored to look like (x-3)(x+2) Now we have on the right of the equal sign: 25 ------------------ (x-3)(x+2) You still following?

  7. anonymous
    • 5 years ago
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    yes

  8. radar
    • 5 years ago
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    Now look at both fractions, notice the denominator on the left is also equal to the denominator on the right of our two fractions that are equal. Do you see that?

  9. anonymous
    • 5 years ago
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    yes i do

  10. radar
    • 5 years ago
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    well since they are equal, then for the two fractions to be equal, the numerators must be equal,so we now can write: x(x-3) + 5(x+2) = 25 Do you follow that kind of reasoning?

  11. anonymous
    • 5 years ago
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    ok i see

  12. radar
    • 5 years ago
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    can you take it from there are do you want me walk you thru the solution.?

  13. anonymous
    • 5 years ago
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    no i can take it from here. thank you very much!

  14. radar
    • 5 years ago
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    O.K and the root equal 3 is extraneous as it results in a division by zero and as you know that is a no-no

  15. anonymous
    • 5 years ago
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    ok, so the final equation before you get (x+5)(x-3) is x^2+2x-15 correct?

  16. radar
    • 5 years ago
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    Yes

  17. anonymous
    • 5 years ago
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    thanks!!

  18. radar
    • 5 years ago
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    NP

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