\(=\dfrac{\left(\sqrt{x}+3\right)^2}{\sqrt{x}+3}+\dfrac{\left(\sqrt{x}-4\right)\cdot\left(\sqrt{x}+4\right)}{\sqrt{x}+4}\)
\(=\sqrt{x}+3+\sqrt{x}-4=2\sqrt{x}-1\)
6) \(\sqrt{x^2+12x+36}=-x-6\)
7) \(\sqrt{9x^2-12x+4}=3x-2\)
8) \(\sqrt{16-24x+9x^2}=2x-10\)
9) \(\sqrt{x^2-6x+9}==2x-3\)
10) \(\sqrt{x^2-3x+\dfrac{9}{4}}=\dfrac{3}{x}x-4\)
Cho Q= \(\dfrac{\sqrt{x}-1}{\sqrt{x}+4}\) + \(\dfrac{9\sqrt{x}-4}{x-16}\) - \(\dfrac{4\sqrt{x}-4x}{\sqrt{x}-4}\)
Chứng minh Q= \(\dfrac{x-3\sqrt{x}}{\sqrt{x}-4}\)
a) \(\sqrt{4x^2-9}=2\sqrt{x+3}\)
b) \(\sqrt{4x+20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
c) \(\dfrac{2}{3}\sqrt{9x-9}-\dfrac{1}{4}\sqrt{16x-16}+27\sqrt{\dfrac{x-1}{81}}=4\)
d)\(5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\)
\(\left(6\right)\dfrac{3\sqrt{x}}{5\sqrt{x}-1}\le-3\)
\(\left(7\right)\dfrac{8\sqrt{x}+8}{6\sqrt{x}+9}>\dfrac{8}{3}\)
\(\left(8\right)\dfrac{\sqrt{x}-2}{2\sqrt{x}-3}< -4\)
\(\left(9\right)\dfrac{4\sqrt{x}+6}{5\sqrt{x}+7}\le-\dfrac{2}{3}\)
\(\left(10\right)\dfrac{6\sqrt{x}-2}{7\sqrt{x}-1}>-6\)
Rút gọn:
1) \(A=\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}-\dfrac{2x+\sqrt{x}}{\sqrt{x}}+1\) với x >1
2) \(A=\dfrac{\sqrt{x}+2}{\sqrt{x}+3}-\dfrac{5}{x+\sqrt{x}-6}+\dfrac{1}{2-\sqrt{x}}\) với x ≠ 4, x ≠16, x >0
Tìm `ĐKXĐ`:
\(\sqrt{\dfrac{-5}{6+x}}\)
\(\sqrt{\dfrac{-2}{6-x}}\)
\(\sqrt{\dfrac{-x+3}{-6}}\)
\(\sqrt{\dfrac{7x-1}{-9}}\)
\(\sqrt{\dfrac{x+2}{x^2+2x+1}}\)
\(\sqrt{\dfrac{x-2}{x^2-2x+4}}\)
Rút gọn:
\(A=\dfrac{\sqrt{x}+2}{\sqrt{x}+3}-\dfrac{5}{x+\sqrt{x}-6}+\dfrac{1}{2-\sqrt{x}}\) với x ≠4, x ≠16, x >0
Thu gọn P
\(P=\dfrac{x-\sqrt{x}}{x-9}+\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-3}\)
a) Tính P biết \(x=\sqrt{6+4\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
b) Tính P biết \(x=\dfrac{1}{\sqrt{2}-1}-\dfrac{1}{\sqrt{2}+1}\)
Rút gọn A=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{2\sqrt{x}+6}{x-9}\right):\dfrac{x-2\sqrt{x}}{\sqrt{x}-3}\) với x>0,x khác 4 và 9
RÚT GỌN BIỂU THỨC:
16) \(A = \dfrac{\sqrt{x}}{\sqrt{x} + 3} + \dfrac{2\sqrt{x}}{\sqrt{x} - 3} - \dfrac{3x + 9}{x - 9}\)
