Question

Rút gọn phân thức

a, \(\frac{x^2-5}{x+\sqrt{5}}\) (x ≠ - \(\sqrt{5}\))

b, \(\frac{a\sqrt{a}-1}{\sqrt{a}-1}+\frac{a^2-1}{\sqrt{a}+1}-a\sqrt{a}\)

c, \(\frac{x^2+2\sqrt{2x}+2}{x^2-2}\)

Answer 1

a/ \(=\frac{\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)}{x+\sqrt{5}}=x-\sqrt{5}\)

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

\(=a+\sqrt{a}+1+\sqrt{a}-1-a\sqrt{a}=a-a\sqrt{a}+2\sqrt{a}\)

c/ Sửa đề bài xíu: \(2\sqrt{2x}\Rightarrow2\sqrt{2}x\)

\(=\frac{\left(x+\sqrt{2}\right)^2}{\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)}=\frac{x+\sqrt{2}}{x-\sqrt{2}}\)

Answer 2

2

Answer 3

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