anonymous
  • anonymous
(a+b)/(a-b)^-1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I have to simplify this complex fraction
DecentNabeel
  • DecentNabeel
\[\frac{a+b}{\left(a-b\right)^{-1}}=\left(a+b\right)\left(a-b\right)\]
anonymous
  • anonymous
a+b/ a^-1 - b^-1 is the actual question

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More answers

DecentNabeel
  • DecentNabeel
\[\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}\] \[\left(a-b\right)^{-1}=\frac{1}{a-b}\] \[=\frac{a+b}{\frac{1}{a-b}}\] \[\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}\] \[\frac{a+b}{\frac{1}{a-b}}=\frac{\left(a+b\right)\left(a-b\right)}{1}\]
DecentNabeel
  • DecentNabeel
\[\frac{a+b}{a^{-1}b^{-1}}=ab\left(a+b\right)\]
DecentNabeel
  • DecentNabeel
that is the question
anonymous
  • anonymous
minus sign between variables in the denomitor
DecentNabeel
  • DecentNabeel
\[\frac{a+b}{a^{-1}-b^{-1}}=\frac{ab\left(a+b\right)}{-a+b}\]
DecentNabeel
  • DecentNabeel
are you ok @ailen
anonymous
  • anonymous
how did you get that
DecentNabeel
  • DecentNabeel
\[\mathrm{Simplify}\:\frac{a+b}{a^{-1}-b^{-1}}:\quad \frac{a+b}{\frac{1}{a}-\frac{1}{b}}\] \[\mathrm{Combine\:the\:fractions\:using\:the\:LCD}:\quad \frac{1}{a}-\frac{1}{b}=\frac{-a+b}{ab}\]
DecentNabeel
  • DecentNabeel
\[=\frac{a+b}{\frac{-a+b}{ab}}\] \[=\frac{ab\left(a+b\right)}{-a+b}\] that is the answer
DecentNabeel
  • DecentNabeel
are you understand @ailen
LynFran
  • LynFran
@DecentNabeel is correct
anonymous
  • anonymous
i totally understood thank you so much
anonymous
  • anonymous
Can you help me on another one please
LynFran
  • LynFran
yes he will lol
anonymous
  • anonymous
(3x+1/x) / (2x - 1/x^2)
LynFran
  • LynFran
https://www.symbolab.com/solver/trigonometric-equation-calculator/%5Cfrac%7B%5Cleft(%5Cfrac%7B3x%2B1%7D%7Bx%7D%5Cright)%7D%7B%5Cleft(%5Cfrac%7B2x-1%7D%7Bx%5E%7B2%7D%7D%5Cright)%7D/?origin=button
anonymous
  • anonymous
Does it show me step by step ?

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