Question

Simplify the complex fraction: (49-x^2)^1/2 + 9x^2(49-x^2)^-1/2 / 49-x^2

Answer 1

[(49 - x^2)^(1/2) + 9x^2(49 - x^2)^(-1/2)] / (49 - x^2)
= (49 - x^2)^(-1/2) * [(49 - x^2) + 9x^2 * 1] / (49 - x^2), via factoring
= (49 + 8x^2) / [(49 - x^2) (49 - x^2)^(1/2)]
= (49 + 8x^2) / (49 - x^2)^(3/2).

I hope this helps!