How do you rationalize the numerator and simplify [(1/sqrtx)+9sqrtx]/(9x+1)(1√x)+9√x9x+1?

1 Answer
Jose Luis F.
Apr 14, 2015

The result is sqrtx/x√xx.

The reason is the following:
1st) You have to rationalize 1/sqrtx1√x. This is done by multiplying both numerator and denominator by sqrtx√x. By doing this, you obtain the following: ((1/sqrtx) + 9sqrtx)/(9x+1) = ((sqrtx/x)+9sqrtx)/(9x+1)(1√x)+9√x9x+1=(√xx)+9√x9x+1.
2nd) Now, you make "x" the common denominator of the numerator as follows:
((sqrtx/x)+9sqrtx)/(9x+1) = ((sqrtx+9xsqrtx)/x)/(9x+1)(√xx)+9√x9x+1=√x+9x√xx9x+1.
3rd) Now, you pass the intermediate "x" to the denominator:
((sqrtx+9xsqrtx)/x)/(9x+1) = (sqrtx+9xsqrtx)/(x(9x+1))√x+9x√xx9x+1=√x+9x√xx(9x+1).
4th) Now, you take common factor sqrtx√x from the numerator:
(sqrtx+9xsqrtx)/(x(9x+1)) = (sqrtx(9x+1))/(x(9x+1)√x+9x√xx(9x+1)=√x(9x+1)x(9x+1).
5th) And, finally, you simplify the factor (9x+1) appearing both in the numerator and the denominator:
(sqrtx(cancel(9x+1)))/(x(cancel(9x+1))) = sqrtx/x.

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
2038 views around the world
You can reuse this answer
Creative Commons License