Question

Rút gọn các biểu thức sau:

a. \(\frac{a-4\sqrt{a}+3}{\sqrt{a}-3}\)

b. \(\frac{a+\sqrt{a^2-6a+9}}{2a-3}với\)\(a\ge3\)

Answer 1

\(a,\frac{a-4\sqrt{a}+4-1}{\sqrt{a}-3}=\frac{\left(\sqrt{a}-2\right)^2-1}{\sqrt{a}-3}.\)

\(=\frac{\left(\sqrt{a}-3\right)\left(\sqrt{a}-1\right)}{\sqrt{a}-3}\)

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

Answer 2

\(b,\frac{a+\sqrt{a^2-6a+9}}{2a-3}=\frac{a+\sqrt{\left(a-3\right)^2}}{2a-3}\)

\(=\frac{a+a-3}{2a-3}=\frac{2a-3}{2a-3}\)

\(=1\)