SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Binomials Containing R

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Question 178262This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Binomials Containing Radicals
Simplify. Assume that each radical represents a real number.
(√w)/(√w+1)+(√w)/(√w-1)

This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28w%29%2F%28sqrt%28w%29%2B1%29%2Bsqrt%28w%29%2F%28sqrt%28w%29-1%29 Start with the given expression.


Take note that the LCD is %28sqrt%28w%29%2B1%29%28sqrt%28w%29-1%29


Multiply the first fraction by %28sqrt%28w%29-1%29%2F%28sqrt%28w%29-1%29 to get the denominator equal to the LCD


Combine and multiply the fractions



Multiply the second fraction by %28sqrt%28w%29%2B1%29%2F%28sqrt%28w%29%2B1%29 to get the denominator equal to the LCD


Combine and multiply the fractions



Distribute


Multiply


Square sqrt%28w%29 to get "w"


%28w-sqrt%28w%29%2Bw%2Bsqrt%28w%29%29%2F%28%28sqrt%28w%29%2B1%29%28sqrt%28w%29-1%29%29 Combine the fractions (this is possible since the denominators are equal)


%282w%29%2F%28%28sqrt%28w%29%2B1%29%28sqrt%28w%29-1%29%29 Combine like terms.


%282w%29%2F%28%28sqrt%28w%29%29%5E2-1%5E2%29 FOIL the denominator (use the difference of squares formula)


%282w%29%2F%28w-1%29 Square sqrt%28w%29 to get "w". Square 1 to get 1



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Answer:


So sqrt%28w%29%2F%28sqrt%28w%29%2B1%29%2Bsqrt%28w%29%2F%28sqrt%28w%29-1%29=%282w%29%2F%28w-1%29 where w%3E=0