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