Đáp án:
$a)P =\dfrac{\sqrt{a}-2}{3\sqrt{a}}\\ b)P(16)=\dfrac{1}{6}$
Giải thích các bước giải:
$a)P=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right) (a>0, a \ne 1, a \ne 4)\\ =\left(\dfrac{\sqrt{a}}{\sqrt{a}(\sqrt{a}-1)}-\dfrac{\sqrt{a}-1}{\sqrt{a}(\sqrt{a}-1)}\right):\left(\dfrac{(\sqrt{a}+1)(\sqrt{a}-1)}{(\sqrt{a}-2)(\sqrt{a}-1)}-\dfrac{(\sqrt{a}+2)(\sqrt{a}-2)}{(\sqrt{a}-1)(\sqrt{a}-2)}\right) \\ =\dfrac{\sqrt{a}-(\sqrt{a}-1)}{\sqrt{a}(\sqrt{a}-1)}:\dfrac{(\sqrt{a}+1)(\sqrt{a}-1)-(\sqrt{a}+2)(\sqrt{a}-2)}{(\sqrt{a}-1)(\sqrt{a}-2)}\\ $$ =\dfrac{1}{\sqrt{a}(\sqrt{a}-1)}:\dfrac{a-1-(a-4)}{(\sqrt{a}-1)(\sqrt{a}-2)}\\ =\dfrac{1}{\sqrt{a}(\sqrt{a}-1)}:\dfrac{3}{(\sqrt{a}-1)(\sqrt{a}-2)}\\ =\dfrac{\sqrt{a}-2}{3\sqrt{a}}\\ b)P(16)=\dfrac{\sqrt{16}-2}{3\sqrt{16}}\\ =\dfrac{4-2}{3.4}\\ =\dfrac{1}{6}$
