Question

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Cho a lớn hơn 0. Rút gọn biểu thức

P=\(\left(\frac{1}{\sqrt{a}}+\frac{1}{a+\sqrt{a}}\right)\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\)

(mik cần gấp)

Answer 1

[✎﹏Kim Kim✧❤‿✶🌈(*•.¸♡ţęąɱ ƒŗęę ƒįŗę...]

\(P=\left(\frac{1}{\sqrt{a}}+\frac{1}{a+\sqrt{a}}\right)\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\)

\(P=\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{a}\left(\sqrt{a}+1\right)}\right)\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\)

\(P=\left(\frac{\sqrt{a}+1+1}{\sqrt{a}\left(\sqrt{a}+1\right)}\right)\cdot\frac{a-1}{\sqrt{a}}\)

\(P=\frac{\sqrt{a}+2}{\sqrt{a}\left(\sqrt{a}+1\right)}\cdot\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}}\)

\(P=\frac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}{a}\)