Problem: The fraction a2+x2−x2−a2a2+x2a2+x2\dfrac{\sqrt{a^{2}+x^{2}}-\dfrac{x^{2}-a^{2}}{\sqrt{a^{2}+x^{2}}}}{a^{2}+x^{2}}a2+x2a2+x2−a2+x2x2−a2 reduces to
Answer Choices:
A. 000
B. 2a2a2+x2\dfrac{2 a^{2}}{a^{2}+x^{2}}a2+x22a2
C. 2x2(a2+x2)3/2\dfrac{2 x^{2}}{\left(a^{2}+x^{2}\right)^{3 / 2}}(a2+x2)3/22x2
D. 2a2(a2+x2)3/2\dfrac{2 a^{2}}{\left(a^{2}+x^{2}\right)^{3 / 2}}(a2+x2)3/22a2
E. 2x2a2+x2\dfrac{2 x^{2}}{a^{2}+x^{2}}a2+x22x2 Solution:
Multiply numerator and denominator by a2+x2\sqrt{a^{2}+x^{2}}a2+x2 and simplify. (D) is the correct choice.