Rút gọn biểu thức :
\(D=\left(\dfrac{\sqrt{a}-2}{\sqrt{a}+2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-2}\right).\left(\sqrt{a}-\dfrac{4}{\sqrt{a}}\right)\) với O<a\(\ne4\)
Câu 1: Rút gọn biểu thức: \(A=\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1-\sqrt{a}}{1-a}\right)^2\)(với a \(\ge\) 0;a \(\ne\)1)
Câu 2: Rút gọn biểu thức: \(M=\left(\dfrac{a+\sqrt{a}}{\sqrt{a}+1}+1\right)\left(1+\dfrac{a-\sqrt{a}}{1-\sqrt{a}}\right)\)(với a\(\ge\)0; a\(\ne\)1)
Câu 2:
Ta có: \(M=\left(\dfrac{a+\sqrt{a}}{\sqrt{a}+1}+1\right)\left(1+\dfrac{a-\sqrt{a}}{1-\sqrt{a}}\right)\)
\(=\left(\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}+1\right)\left(1-\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)\)
\(=1-a\)
Câu 1:
Ta có: \(A=\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1-\sqrt{a}}{1-a}\right)^2\)
\(=\left(\dfrac{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1}{\sqrt{a}+1}\right)^2\)
\(=\left(\sqrt{a}+1\right)^2\cdot\dfrac{1}{\left(\sqrt{a}+1\right)^2}\)
\(=1\)
Rút gọn các biểu thức:
\(A=\left(\dfrac{1}{\sqrt{x}+2}+\dfrac{1}{\sqrt{x}-2}\right):\dfrac{x-4}{3\sqrt{x}}\)
\(B=\left(\dfrac{\sqrt{a}}{\sqrt{a}-2}+\dfrac{1}{\sqrt{a}+2}+\dfrac{6-7\sqrt{a}}{a-4}\right).\left(\sqrt{a}+2\right)\)
a: Ta có: \(A=\left(\dfrac{1}{\sqrt{x}+2}+\dfrac{1}{\sqrt{x}-2}\right)\cdot\dfrac{x-4}{3\sqrt{x}}\)
\(=\dfrac{\sqrt{x}-2+\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\cdot\dfrac{x-4}{3\sqrt{x}}\)
\(=\dfrac{2}{3}\)
A=\(\left(\dfrac{a+4\sqrt{a}+4}{a+2\sqrt{a}}-\dfrac{\sqrt{a}}{\sqrt{a}-2}\right):\left(\dfrac{\sqrt{a}-4}{a-2\sqrt{a}}-\dfrac{3\sqrt{a}+6}{4-a}\right)\)
Rút gọn biểu thức trên
Ta có:\(A=\left(\dfrac{a+4\sqrt{a}+4}{a+2\sqrt{a}}-\dfrac{\sqrt{a}}{\sqrt{a}-2}\right):\left(\dfrac{\sqrt{a}-4}{a-2\sqrt{a}}-\dfrac{3\sqrt{a}+6}{4-a}\right)\)
\(=\left[\dfrac{\left(\sqrt{a}+2\right)^2}{\sqrt{a}\left(\sqrt{a}+2\right)}-\dfrac{\sqrt{a}}{\sqrt{a}-2}\right]:\left[\dfrac{\sqrt{a}-4}{\sqrt{a}\left(\sqrt{a}-2\right)}+\dfrac{3\left(\sqrt{a}+2\right)}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}\right]\)
\(=\dfrac{a-4-a-2\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-2\right)}:\dfrac{\sqrt{a}-4+3\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-2\right)}\)
\(=\dfrac{-4-2\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-2\right)}.\dfrac{\sqrt{a}\left(\sqrt{a}-2\right)}{4\sqrt{a}-4}=\dfrac{-2-\sqrt{a}}{2\sqrt{a}-2}\)
Ta có: \(A=\left(\dfrac{a+4\sqrt{a}+4}{a+2\sqrt{a}}-\dfrac{\sqrt{a}}{\sqrt{a}-2}\right):\left(\dfrac{\sqrt{a}-4}{a-2\sqrt{a}}-\dfrac{3\sqrt{a}+6}{4-a}\right)\)
\(=\left(\dfrac{\sqrt{a}+2}{\sqrt{a}}-\dfrac{\sqrt{a}}{\sqrt{a}-2}\right):\left(\dfrac{\sqrt{a}-4}{\sqrt{a}\left(\sqrt{a}-2\right)}+\dfrac{3}{\sqrt{a}-2}\right)\)
\(=\dfrac{a-4-a}{\sqrt{a}\left(\sqrt{a}-2\right)}:\dfrac{\sqrt{a}-4+3\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-2\right)}\)
\(=\dfrac{-4}{4\left(\sqrt{a}+1\right)}=\dfrac{-1}{\sqrt{a}+1}\)
Rút gọn các biểu thức sau:
\(A=\dfrac{a^2-1}{3}\sqrt{\dfrac{9}{\left(1-a\right)^2}}\) với a < 1
\(B=\sqrt{\left(3a-5\right)^2}-2a+4\) với a < \(\dfrac{1}{2}\)
\(C=4a-3-\sqrt{\left(2a-1\right)^2}\) với a < 2
\(D=\dfrac{a-2}{4}\sqrt{\dfrac{16a^4}{\left(a-2\right)^2}}\) với a < 2
a) Ta có: \(A=\dfrac{a^2-1}{3}\cdot\sqrt{\dfrac{9}{\left(1-a\right)^2}}\)
\(=\dfrac{\left(a+1\right)\cdot\left(a-1\right)}{3}\cdot\dfrac{3}{\left|1-a\right|}\)
\(=\dfrac{\left(a+1\right)\left(a-1\right)}{1-a}\)
=-a-1
b) Ta có: \(B=\sqrt{\left(3a-5\right)^2}-2a+4\)
\(=\left|3a-5\right|-2a+4\)
\(=5-3a-2a+4\)
=9-5a
c) Ta có: \(C=4a-3-\sqrt{\left(2a-1\right)^2}\)
\(=4a-3-\left|2a-1\right|\)
\(=4a-3-2a+1\)
\(=2a-2\)
d) Ta có: \(D=\dfrac{a-2}{4}\cdot\sqrt{\dfrac{16a^4}{\left(a-2\right)^2}}\)
\(=\dfrac{a-2}{4}\cdot\dfrac{4a^2}{\left|a-2\right|}\)
\(=\dfrac{a^2\left(a-2\right)}{-\left(a-2\right)}\)
\(=-a^2\)
1. Cho biểu thức: A=\(\left[\dfrac{a+3\sqrt{a}+2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}-\dfrac{a+\sqrt{a}}{a-1}\right]:\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{1}{\sqrt{a}-1}\right)\)
Rút gọn biểu thức trên
A=\(\left[\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}+1\right)}{\left(a-1\right)\left(\sqrt{a}+2\right)}-\dfrac{\left(a+\sqrt{a}\right)}{\left(a-1\right)}\right]\)::::::::\(\left(\dfrac{\left(\sqrt{a}-1+\sqrt{a}+1\right)}{a-1}\right)\)
=\(\left[\dfrac{1}{\sqrt{a}-1}\right]:\left(\dfrac{2\sqrt{a}}{a-1}\right)\)=\(\dfrac{\sqrt{a}-1}{2\sqrt{a}}\)
=\(\dfrac{a^2+a\sqrt{a}+11a+6}{2\sqrt{a}\left(\sqrt{a}+2\right)}\)
Ta có: \(A=\left(\dfrac{a+3\sqrt{a}+2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}-\dfrac{a+\sqrt{a}}{a-1}\right):\left(\dfrac{1}{\sqrt{a}+1}+\dfrac{1}{\sqrt{a}-1}\right)\)
\(=\dfrac{\sqrt{a}+1-\sqrt{a}}{\sqrt{a}-1}:\dfrac{\sqrt{a}-1+\sqrt{a}+1}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\)
\(=\dfrac{1}{\sqrt{a}-1}\cdot\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{2\sqrt{a}}\)
\(=\dfrac{\sqrt{a}+1}{2\sqrt{a}}\)
rút gọn biểu thức
\(G=\dfrac{\sqrt[3]{a}.a^{\dfrac{2}{3}}}{\left(a^{4-2\sqrt{3}}\right)^{4+2\sqrt{3}}}\)
\(G=\dfrac{a^{\sqrt{7}+1}.a^{2-\sqrt{7}}}{\left(a^{\sqrt{2}-2}\right)^{\sqrt{2}+2}}\)
\(H=\dfrac{a^2.\left(a^{-2}.b^3\right).b^{-1}}{\left(a^{-1}.b\right)^3.a^{-5}.b^{-2}}\)
\(H=\dfrac{b^3.a^{-4}.\left(ab^2\right)^3}{\left(a^2\right)^{-2}.\left(ab^3\right)^2.b^2}\)
\(H=\dfrac{b^3.a^{-4}.\left(ab^2\right)^3}{\left(a^2\right)^{-2}.\left(ab^3\right)^2.b^2}\)
\(H=\dfrac{b^3.a^{-4}.\left(ab^2\right)^3}{\left(a^2\right)^{-2}.\left(ab^3\right)^2.b^2}\)
Rút gọn các biểu thức sau:
\(C=\left(\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{\sqrt{a}}{a-\sqrt{1}}\right):\dfrac{\sqrt{a}+1}{a-1}\)
\(D=\left(\dfrac{x-2}{x+2\sqrt{x}}+\dfrac{1}{\sqrt{x}+2}\right).\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(E=\left(1+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\)
Làm ơn giúp mình với ạ!!mình đang cần gấp lắm!!
rút gọn biểu thức A=\(\dfrac{\left(2-\sqrt{a}\right)-\left(\sqrt{a+3}\right)}{1+2\sqrt{a}}\) (với a>0) ; B=\(\dfrac{1}{1-\sqrt{2}+\sqrt{3}}-\dfrac{1}{1-\sqrt{2-\sqrt{3}}}\); C=\(\dfrac{1}{\sqrt{5-2}}+\dfrac{1}{\sqrt{5+\sqrt{2}}}\)
\(A=\dfrac{2-\sqrt{a}-\sqrt{a}-3}{2\sqrt{a}+1}=-1\)
\(B=\dfrac{1}{1-\sqrt{2+\sqrt{3}}}-\dfrac{1}{1-\sqrt{2-\sqrt{3}}}\)
\(=\dfrac{\sqrt{2}}{\sqrt{2}-\sqrt{3}-1}-\dfrac{\sqrt{2}}{\sqrt{2}-\sqrt{3}+1}\)
\(=\dfrac{2-\sqrt{6}+\sqrt{2}-2+\sqrt{6}+\sqrt{2}}{5-2\sqrt{6}-1}\)
\(=\dfrac{2\sqrt{2}}{4-2\sqrt{6}}=\dfrac{1}{\sqrt{2}-\sqrt{3}}=-\sqrt{2}-\sqrt{3}\)
Rút gọn các biểu thức sau:
\(A=\left(\dfrac{1}{\sqrt{a}+2}+\dfrac{1}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}}{a-4}\)
\(B=\left(\dfrac{4x}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{x-3\sqrt{x}+2}\right).\dfrac{\sqrt{x}-1}{x^2}\)
\(C=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{x-9}\right).\dfrac{2\sqrt{x}+6}{\sqrt{x}-1}\)
\(D=\left(\dfrac{5\sqrt{x}-6}{x-9}-\dfrac{2}{\sqrt{x}+3}\right):\left(1+\dfrac{6}{x-9}\right)\)
\(E=\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{9+x}{9-x}\right).\left(3\sqrt{x}-x\right)\)
help
Rút gọn các biểu thức sau:
\(A=\left(\dfrac{1}{\sqrt{a}+2}+\dfrac{1}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}}{a-4}\)
\(B=\left(\dfrac{4x}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{x-3\sqrt{x}+2}\right).\dfrac{\sqrt{x}-1}{x^2}\)
\(C=\left(\dfrac{1}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{x-9}\right).\dfrac{2\sqrt{x}+6}{\sqrt{x}-1}\)
\(D=\left(\dfrac{5\sqrt{x}-6}{x-9}-\dfrac{2}{\sqrt{x}+3}\right):\left(1+\dfrac{6}{x-9}\right)\)
\(E=\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{9+x}{9-x}\right).\left(3\sqrt{x}-x\right)\)
help
a) Ta có: \(A=\left(\dfrac{1}{\sqrt{a}+2}+\dfrac{1}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}}{a-4}\)
\(=\dfrac{\sqrt{a}-2+\sqrt{a}+2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\cdot\dfrac{\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}{\sqrt{a}}\)
=2
b) Ta có: \(B=\left(\dfrac{4x}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{x-3\sqrt{x}+2}\right)\cdot\dfrac{\sqrt{x}-1}{x^2}\)
\(=\dfrac{4x-1}{\sqrt{x}-1}\cdot\dfrac{\sqrt{x}-1}{x^2}\)
\(=\dfrac{4x-1}{x^2}\)