Question

Rút gọn

a)\(\dfrac{2}{\sqrt{5}-\sqrt{3}}+\dfrac{3}{\sqrt{5}+\sqrt{3}}\)

b)\(\dfrac{a-\sqrt{b}}{\sqrt{b}}:\dfrac{\sqrt{b}}{a+\sqrt{b}}\)

c)\(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{a^3}-\sqrt{b^3}}{a-b}\left(a,b\ge0,a\ne b\right)\)

Answer 1

a)\(\dfrac{2}{\sqrt{5}-\sqrt{3}}+\dfrac{3}{\sqrt{5}+\sqrt{3}}=\dfrac{2\sqrt{5}+2\sqrt{3}+3\sqrt{5}-3\sqrt{3}}{5-3}=\dfrac{5\sqrt{5}-\sqrt{3}}{2}\)

Answer 2

a) \(\dfrac{2}{\sqrt{5}-\sqrt{3}}+\dfrac{3}{\sqrt{5}+\sqrt{3}}\)

= \(\dfrac{2\sqrt{5}+2\sqrt{3}+3\sqrt{5}-3\sqrt{3}}{5-3}\)

= \(\dfrac{5\sqrt{5}-\sqrt{3}}{2}\)

Answer 3

b)\(\dfrac{a-\sqrt{b}}{\sqrt{b}}:\dfrac{\sqrt{b}}{a+\sqrt{b}}\)

= \(\dfrac{\left(a-\sqrt{b}\right).\left(a+\sqrt{b}\right)}{\sqrt{b}\sqrt{b}}\)

= \(\dfrac{a^2-b}{b}\)

Answer 4

c) \(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}-\dfrac{\sqrt{a^3}-\sqrt{b^3}}{a-b}\)

= \(\dfrac{a\sqrt{a}+a\sqrt{b}-b\sqrt{a}-b\sqrt{b}-\sqrt{a^3}+\sqrt{b^3}}{a-b}\)

= \(\dfrac{\sqrt{a^3}+\sqrt{a^2b}-\sqrt{ab^2}-\sqrt{b^3}-\sqrt{a^3}+\sqrt{b^3}}{a-b}\)

= \(\dfrac{\sqrt{a^2b}-\sqrt{ab^2}}{a-b}\)

Answer 5

mik làm hơi tắt ko bt có sai j ko :")