Answer
$5 \sqrt 2+5$
Work Step by Step
Rationalize the denominator by multiplying $\sqrt2+1$ to both the numerator and the denominator:
$\dfrac{5}{\sqrt 2-1}=\dfrac{5}{\sqrt 2-1} \cdot \dfrac{\sqrt 2+1}{\sqrt 2+1}$
Use distributive property in the numerator and special formula $(a+b)(a-b)=a^2-b^2$ in the denominator.
$=\dfrac{5\cdot \sqrt 2+5\cdot1}{(\sqrt 2)^2-1^2}$
$=\dfrac{5\sqrt 2+5}{(\sqrt 2)^2-1}$
Use the rule $(\sqrt{a})^2=a, a>0$ to obtain:
$=\dfrac{5 \sqrt 2+5}{2-1}$
$=\dfrac{5 \sqrt 2+5}{1}$
$=5 \sqrt 2+5$
Hence, the correct answer is $5 \sqrt 2+5$.
