If I have an expression such as $\frac{(1-a)}{a(a-1)}$ am I allowed to distribute a negative sign only to the denominator, and if so why. How does the negative sign distribute over both factors that is $(a)(a-1)$? Is that not allowed?

  • 1
    $\begingroup$ You could substitute $(1-a) = -(a-1)$ and then cancel out the $(a-1)$ of the numerator with the one in the denominator, leaving $-1/a$ $\endgroup$ – Sak Apr 1 '14 at 19:00
  • $\begingroup$ What a blessing you are. Thank you. I was under the impression that people were multiplying the denominator by -1; which made no sense to me. Nonetheless, so that I can have a deeper understanding, is there any other way to arrive at -1/a? $\endgroup$ – Prologue Apr 1 '14 at 19:13

Both ways are correct since they lead to the same result: $$\require{cancel} \dfrac{(1-a)}{a(a-1)}=\dfrac{-\cancel{(a-1)}}{a\cancel{(a-1)}}=-\dfrac1a \\ \color{grey}{\text{or }}\dfrac{(1-a)}{a(a-1)}=\dfrac{\cancel{(1-a)}}{-a\cancel{(1-a)}}=\dfrac1{-a}=-\dfrac1a. $$

I hope this helps.
Best wishes, $\mathcal H$akim.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.