Add and simplify. 1/(x^2)(sqrt{x^2+1}) + 1/sqrt{x^2+1}

+2 votes
asked Dec 23, 2012 in Mathematics by FLoops ~Expert~ (2,117 points)
    

1 Answer

0 votes

rewritten with a power of (1/2) instead of sqrt{}  

                  1                        +                            1


x^2 * (x^2 +1)^(1/2)                     +             (x^2+1)^(1/2)

 

Make common denominators (necessary for fraction addition):

                     1                       +                          x^2


x^2 * (x^2 +1)  ^(1/2)                   +             x^2 * (x^2 +1)^(1/2)

Combine with fraction addition (keep bottom(denominators) the same and add the tops(numerators))

1+x^2


x^2*(x^2+1)^(1/2)

 

change sign of exponent on bottom and raise it to the top:

(1+x^2)(1+x^2)^(-1/2)


x^2

Use exponent addition which states (x^m)*(x^n)=x^(m+n):

(1+x^2)^(1-(1/2))


x^2

simplify:

(1+x^2)^(1/2)


x^2

The answer is: sqrt{1+x^2}/x^2

answered Oct 21, 2015 by reedinationer ~Rookie~ (102 points)

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