Answer
$\dfrac{xy}{x+y}$
Work Step by Step
Let's note:
$$E=(x^{-1}+y^{-1})^{-1}.$$
Rewrite the expression clearing the negative exponents:
$$E=\dfrac{1}{x^{-1}+y^{-1}}=\dfrac{1}{\dfrac{1}{x}+\dfrac{1}{y}}$$
Multiply both numerator and denominator by $xy$ and simplify:
$$E=\dfrac{xy}{xy\left(\dfrac{1}{x}+\dfrac{1}{y}\right)}=\dfrac{xy}{y+x}$$
