cho bieu thuc P= (\(\frac{3x+\sqrt{9x}-3}{x+\sqrt{x}-2}+\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}-3}\) ): \(\frac{1}{x-1}\)
a) Tim dieu kien de P co nghia, rut gon bieu thuc P.
b) Tim cac so tu nhien x de \(\frac{1}{P}\)la so tu nhien
c) Tinh gia tri cua P voi x= 4-\(2\sqrt{3}\)
Giup mk vs mk dang can gap
Cho bieu thuc A=\(\left(\dfrac{4}{x-\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}-1}\right)\div\dfrac{1}{\sqrt{x}-1}\)
a/ Tim dieu kien cua x de bieu thuc A co gia tri xac dinh
b/ Rut gon A
c/ Tinh gia tri cua A khi x = \(4-2\sqrt{3}\)
d/ Tim gia tri nho nhat cua A
Cho cac bieu thuc :
\(A=\dfrac{\sqrt{x}+4}{\sqrt{x}+2},B=\left(\dfrac{\sqrt{x}}{\sqrt{x}+4}+\dfrac{4}{\sqrt{x}-4}\right):\dfrac{x+16}{\sqrt{x}+2}\)
a) Rut gon B ?
b) Tim cac gia tri nguyen cua x de cac gia tri cua bieu thuc B(A-1) la so nguyen.
Cho bthuc: \(A=\frac{1}{2\sqrt{x}-2}-\frac{1}{2\sqrt{x}+2}+\frac{\sqrt{x}}{1-x}\)
a) Rut gon A
b) Tim gia tri cua x de /A/ =\(\frac{1}{2}\)
c) Tim x nguyen de A co gia tri nguyen
cho bieu thuc A=\(\left(\dfrac{6x+4}{3\sqrt{3x^3}-8}-\dfrac{\sqrt{3x}}{3x+2\sqrt{3x}+4}\right)\left(\dfrac{1+3\sqrt{3x^3}}{1+\sqrt{3x}}-\sqrt{3x}\right)\)
a.rut gon bieu thuc A
b. tim cac gia tri nguyen x de A nguyen
\(\dfrac{1}{\sqrt{x}-1}-\dfrac{3}{x\sqrt{x}+1}+\dfrac{1}{x-\sqrt{x}+1}\)
a) Rut gon
b) Tim gia tri cua x de C < 1
cho bieu thuc P=(\(\dfrac{1}{x+2\sqrt{x}}-\dfrac{1}{\sqrt{x}+2}\)): \(\dfrac{1-\sqrt{x}}{x+4\sqrt{x}+4}\) (với x>0, x khác 1)
a. rut gon bieu thuc P
b. Tìm x để P=\(\dfrac{4}{3}\)
Cho bieu thuc E= \(\left(\dfrac{2x\sqrt{x}+x-\sqrt{x}}{x\sqrt{x}-1}-\dfrac{x+\sqrt{x}}{x-1}\right).\dfrac{x-1}{2x+\sqrt{x}-1}+\dfrac{\sqrt{x}}{2\sqrt{x}-1}\)
a)Rut gon E
b)Tim GTNN cua E
c) Tìm x để E ≥ \(\dfrac{6}{7}\)
(\(\dfrac{1}{\sqrt{x}-\sqrt{x-1}}-\dfrac{x-3}{\sqrt{x-1}-\sqrt{2}})\left(\dfrac{2}{2-\sqrt{x}}-\dfrac{\sqrt{x}+\sqrt{2}}{2\sqrt{x}-x}\right)\)
Rut gon bieu thuc
\(P=\left(\dfrac{3x+\sqrt{9x}-3}{x+\sqrt{x}-2}-\dfrac{\sqrt{x}+1}{\sqrt{x}+2}+\dfrac{\sqrt{x}-2}{\sqrt{x}}\right).\left(\dfrac{1}{1-\sqrt{x}}-1\right)\)
a, rut gon
b, tim x de P=\(\sqrt{x}\)