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anonymous

  • one year ago

(a+b)/(a-b)^-1

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  1. anonymous
    • one year ago
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    I have to simplify this complex fraction

  2. DecentNabeel
    • one year ago
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    \[\frac{a+b}{\left(a-b\right)^{-1}}=\left(a+b\right)\left(a-b\right)\]

  3. anonymous
    • one year ago
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    a+b/ a^-1 - b^-1 is the actual question

  4. DecentNabeel
    • one year ago
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    \[\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}\] \[\left(a-b\right)^{-1}=\frac{1}{a-b}\] \[=\frac{a+b}{\frac{1}{a-b}}\] \[\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}\] \[\frac{a+b}{\frac{1}{a-b}}=\frac{\left(a+b\right)\left(a-b\right)}{1}\]

  5. DecentNabeel
    • one year ago
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    \[\frac{a+b}{a^{-1}b^{-1}}=ab\left(a+b\right)\]

  6. DecentNabeel
    • one year ago
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    that is the question

  7. anonymous
    • one year ago
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    minus sign between variables in the denomitor

  8. DecentNabeel
    • one year ago
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    \[\frac{a+b}{a^{-1}-b^{-1}}=\frac{ab\left(a+b\right)}{-a+b}\]

  9. DecentNabeel
    • one year ago
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    are you ok @ailen

  10. anonymous
    • one year ago
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    how did you get that

  11. DecentNabeel
    • one year ago
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    \[\mathrm{Simplify}\:\frac{a+b}{a^{-1}-b^{-1}}:\quad \frac{a+b}{\frac{1}{a}-\frac{1}{b}}\] \[\mathrm{Combine\:the\:fractions\:using\:the\:LCD}:\quad \frac{1}{a}-\frac{1}{b}=\frac{-a+b}{ab}\]

  12. DecentNabeel
    • one year ago
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    \[=\frac{a+b}{\frac{-a+b}{ab}}\] \[=\frac{ab\left(a+b\right)}{-a+b}\] that is the answer

  13. DecentNabeel
    • one year ago
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    are you understand @ailen

  14. LynFran
    • one year ago
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    @DecentNabeel is correct

  15. anonymous
    • one year ago
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    i totally understood thank you so much

  16. anonymous
    • one year ago
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    Can you help me on another one please

  17. LynFran
    • one year ago
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    yes he will lol

  18. anonymous
    • one year ago
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    (3x+1/x) / (2x - 1/x^2)

  19. anonymous
    • one year ago
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    Does it show me step by step ?

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