I require help to simplify this. I used the method to make the denominator a single fraction then multiply the top by the reciprocal but when it comes to cancelling, I'm not sure if i've done it right. (1)/((x^2)+x+2)/(1+(2)/(x((x^2)+x+2)))

agantisbz 2022-07-18 Answered
Help to simplify this complicated fraction
I require help to simplify this. I used the method to make the denominator a single fraction then multiply the top by the reciprocal but when it comes to cancelling, I'm not sure if i've done it right.
1 x 2 + x + 2 1 + 2 x ( x 2 + x + 2 )
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Killaninl2
Answered 2022-07-19 Author has 20 answers
Assuming x 0 and x 2 + x + 2 0 (the latter is always the case):
1 x 2 + x + 2 1 + 2 x ( x 2 + x + 2 ) x ( x 2 + x + 2 ) x ( x 2 + x + 2 ) = x x ( x 2 + x + 2 ) + 2
It is not possible to simplify this further, if not by factorizing the denominator. Please keep in mind the conditions I've put in the beginning.
EDIT: factorization leads to the final answer:
x ( x + 1 ) ( x 2 + 2 )
Only for non-zero x; now that you've got an explicit form of the fraction, you can put existence conditions. In this case, x 0 and x 1
Did you like this example?
Subscribe for all access
jlo2ni5x
Answered 2022-07-20 Author has 8 answers
1 x 2 + x + 2 1 + 2 x ( x 2 + x + 2 ) = x x ( x 2 + x + 2 ) + 2 = x ( x + 1 ) ( x 2 + 2 )
where x 1
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in