Question

Rút Gọn Biểu Thức

1, \(\dfrac{a-6\sqrt{a}+9}{5\sqrt{a}-15}\) với a≥0, a≠9

2.\(5x-\sqrt{x^2-10x+25}\) với x nhỏ hơn 5

3,\(\dfrac{\sqrt{x^2-2x+1}}{x-1}\) với x≠1

4, 3√5 \(\sqrt{46-6v5}\)

Answer 1

1) Ta có: \(\dfrac{a-6\sqrt{a}+9}{5\sqrt{a}-15}\)

\(=\dfrac{\left(\sqrt{a}-3\right)^2}{5\left(\sqrt{a}-3\right)}\)

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

2) Ta có: \(5x-\sqrt{x^2-10x+25}\)

\(=5x-\left|x-5\right|\)

\(=5x-5+x\)

=6x-5

3) Ta có: \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\)

\(=\dfrac{\left|x-1\right|}{\left(x-1\right)\left(x+1\right)}\)

\(=\dfrac{\pm1}{x+1}\)

4) Ta có: \(3\sqrt{5}-\sqrt{46-6\sqrt{5}}\)

\(=3\sqrt{5}-3\sqrt{5}+1\)

=1