ĐKXĐ: \(x\ge1\)
\(=\sqrt{x+2-2\sqrt{\left(x-1\right)\left(x+2\right)}+x-1}\)
\(=\sqrt{\left(\sqrt{x+2}-\sqrt{x-1}\right)^2}\)
\(=\sqrt{x+2}-\sqrt{x-1}\)
Rut gon bt C=\(\dfrac{\sqrt{4x+4+\dfrac{1}{x}}}{\sqrt{x}.\left|2x^2-x-1\right|}\)
cho P=\(\left(\dfrac{3}{\sqrt{x}-1}+\dfrac{\sqrt{x}-3}{x-1}\right):\left(\dfrac{x+2}{x+\sqrt{x}-2}-\dfrac{\sqrt{x}}{\sqrt{x}+2}\right)\\ \)
a, rut gon
b, tim x de P=\(\sqrt{x}-1\)
Cho A = \(\left(\dfrac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}+\dfrac{\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}\right):\left(1+\dfrac{x+y+2xy}{1-xy}\right)\)
a, Rut gon bieu thuc A
b, Tinh gia tri cua A khi x = \(\dfrac{1}{1+\sqrt{2}}\)
c, Tim Max A
B=\(\left(\frac{1}{x+\sqrt{x}}+\frac{1}{\sqrt{x}+1}-1\right):\frac{\sqrt{x}-1}{\sqrt{x}-2}\)
a,Rut gon B
b,Tim cac gia tri cua x de 3B=\(2\sqrt{x}-7\)
Bai tap: Cho:
\(A=\left(\dfrac{1}{x+\sqrt{x}}+\dfrac{1}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}-1}{x+2\sqrt{x}+1}+1\)
a) Rut gon
b) Tinh gia tri cua A voi \(x=1\dfrac{1}{3}\)
\(\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}:\frac{2}{x^2-2x+1}\) các bạn giúp mình rút gọn với ạ
Rút gon
\(J=\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{\sqrt{x}-1}{\sqrt{x}+1}\right):\left(1-\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)\)
\(K=\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}\right):\left(\frac{1}{1+\sqrt{x}}+\frac{2}{x-1}\right)\)
\(I=\left(\frac{\sqrt{a}-2}{a-1}-\frac{\sqrt{a}+2}{a+2\sqrt{a}+1}\right).\left(1+\frac{1}{\sqrt{a}}\right)\)
Giúp mk với các cao nhân ơi,mk xin cảm on nhiều. Mk sẽ tick cho.
P=\(\dfrac{1}{2\left(1+\sqrt{a}\right)}+\dfrac{1}{2\left(1-\sqrt{a}\right)}-\dfrac{a^2+2}{1-a^2}\)
a rut gon P
b tìm a để P =\(\dfrac{7}{8}\)
M=\(\left(\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}\right):\left(\frac{2}{x}-\frac{2-x}{x\sqrt{x}+x}\right)\)
Rút gon biểu thức M
Tính x để M=2
