SOLUTION: I was trying to solve this problem, I tried rationalizing the denominator but I could not eliminate the middle terms in the denominator because the exponents of the variable inside
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Question 154073: I was trying to solve this problem, I tried rationalizing the denominator but I could not eliminate the middle terms in the denominator because the exponents of the variable inside the cube root sign is not the same. I took this problem from the College Algebra book by William Hart, 4th Edition. This is under exercise 53, problem number 148, page 127. This is the problem:
If only the index of the radicals in the denominator is equal to 2,and not a 3 (which is a cube root) I could immediately perform rationalization.
I hope somebody could help me.
thanks and best regards,
jomar
To rationalize the denominator when the denominator is the
difference of cube roots, you must use the factorization of
the difference of cubes formula.
But write the left side on the right and vice-versa, so you
can better see what to do:
Let A and B be the terms of the denominator:
,
Substituting into ,
Simplifying,
So as you can see from that, to rationalize the denominator,
you must multiply top and bottom by
which can be simplified a little:
We have just finished multiplying the bottom by that
and gotten the rational expression .
Now we must multiply the numerator, which is
by it too:
=
=
Combine like terms:
Now put this over the denominator which we rationalized
first:
Edwin
