Bài 1: Căn bậc hai
Các câu hỏi tương tự
a,cmr \(\left(\sqrt{a}+\dfrac{b-\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\right):\left(\dfrac{a}{\sqrt{ab}+b}+\dfrac{b}{\sqrt{ab}-a}-\dfrac{a+b}{\sqrt{ab}}\right)=\sqrt{b}-\sqrt{a}\)
b, A=\((\dfrac{a-\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}+1}{a+\sqrt{a}}):\dfrac{\sqrt{a}+1}{a}\)
1.tìm đk của A để A có ngĩa
2.rút gọn A
3.tìm GTNN của A
rút gọn:
A=\(x-4-\sqrt{16-8x^2+x^4}\left(x>4\right)\)
B=\(\dfrac{a+b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}:\dfrac{1}{\sqrt{a}+\sqrt{b}}\left(a,b>0,a\ne b\right)\)
Cho A=\(\sqrt{a}+\dfrac{b-\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\)
B=\(\dfrac{a}{\sqrt{ab}+b}+\dfrac{b}{\sqrt{ab}-a}-\dfrac{a+b}{\sqrt{ab}}\)
a) rút gọn A,B
b)tìm a,b để \(\dfrac{A}{B}>0\)
Thu gọn :
\(\left(\dfrac{a-4b}{\sqrt{a}+2\sqrt{b}}\right):\dfrac{\sqrt{ab}}{a\sqrt{b}+b\sqrt{a}}\)
Rút gọn các biểu thức saua,Aleft(dfrac{1}{x-sqrt{x}}+dfrac{1}{sqrt{x}-1}right):dfrac{sqrt{x}+1}{x-2sqrt{x}+1}b,Bdfrac{2sqrt{x}-1}{sqrt{x}+1}+dfrac{3sqrt{x}-1}{x-sqrt{x}+1}-dfrac{2xsqrt{x}-2x+2sqrt{x}-3}{xsqrt{x}+1}c,Cleft(1-dfrac{x+3sqrt{x}}{x-9}right):left(dfrac{sqrt{x}-3}{2-sqrt{x}}+dfrac{sqrt{x}-2}{3+sqrt{x}}-dfrac{9-x}{x+sqrt{x}-6}right)d,Dleft(dfrac{sqrt{x}}{3+sqrt{x}}+dfrac{x+9}{9-x}right):left(dfrac{3sqrt{x}+1}{x-3sqrt{x}}-dfrac{1}{sqrt{x}}right)e,Edfrac{15sqrt{x}-11}{x+2sqrt{x}-3}+dfrac{...
Đọc tiếp
Rút gọn các biểu thức sau
a,\(A=\left(\dfrac{1}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}+1}{x-2\sqrt{x}+1}\)
b,\(B=\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}+\dfrac{3\sqrt{x}-1}{x-\sqrt{x}+1}-\dfrac{2x\sqrt{x}-2x+2\sqrt{x}-3}{x\sqrt{x}+1}\)
c,\(C=\left(1-\dfrac{x+3\sqrt{x}}{x-9}\right):\left(\dfrac{\sqrt{x}-3}{2-\sqrt{x}}+\dfrac{\sqrt{x}-2}{3+\sqrt{x}}-\dfrac{9-x}{x+\sqrt{x}-6}\right)\)
d,\(D=\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{x+9}{9-x}\right):\left(\dfrac{3\sqrt{x}+1}{x-3\sqrt{x}}-\dfrac{1}{\sqrt{x}}\right)\)
e,\(E=\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(\dfrac{a\sqrt{b}+b\sqrt{a}}{\sqrt{ab}}\):\(\dfrac{1}{\sqrt{a}-\sqrt{b}}\)
Rút gọn
Rút gọn:
B= \(\left(2-\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\dfrac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)\)
1. cho P = \(\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{2\sqrt{a}}{a-1}+\dfrac{\sqrt{a}}{a+1}\right):\dfrac{\sqrt{a}}{\sqrt{a}+1}\)
a. Rút gọn P
b. Tìm a để P < \(\dfrac{1}{2}\)
\(P=\left(\dfrac{3x+3\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}+\dfrac{1}{\sqrt{x}+2}-\dfrac{\sqrt{x}-2}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+1}\)
a) Rút gọn P (x > o, x khác 1)
b) Tìm giá trị của x để P > 0