Cho bt : \(P=\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right):\left(\frac{\sqrt{x}-3}{2\sqrt{x}-x}\right)\)
Rút gọn P
D=\(\left(\frac{\sqrt{x}+2}{2-\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+2}-\frac{4x+2\sqrt{x}-4}{x-4}\right)/\left(\frac{2}{2-\sqrt{x}}-\frac{3+\sqrt{x}}{2\sqrt{x}-x}\right)\)
Rút gọn giúp với,...
rút gọn bthức sau
\(\left(\frac{2}{2-\sqrt{x}}+\frac{3+\sqrt{x}}{x-2\sqrt{x}}\right):\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right)\)
\(ĐKXĐ:x\ge0\)
\(\left(\frac{2}{2-\sqrt{x}}+\frac{3+\sqrt{x}}{x-2\sqrt{x}}\right):\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right)\)
\(=\frac{-2\sqrt{x}}{x-2\sqrt{x}}:\frac{\left(2+\sqrt{x}\right)^2-\left(2-\sqrt{x}\right)^2+4x}{4-x}\)
\(=\frac{-2\sqrt{x}}{x-2\sqrt{x}}:\frac{\left(4+4\sqrt{x}+x\right)-\left(4-4\sqrt{x}+x\right)+4x}{4-x}\)
\(=\frac{-2\sqrt{x}}{x-2\sqrt{x}}:\frac{8\sqrt{x}+4x}{4-x}\)
\(=\frac{-2\sqrt{x}}{x-2\sqrt{x}}.\frac{4-x}{8\sqrt{x}+4x}\)
\(=\frac{2\sqrt{x}\left(\sqrt{x}-2\right)\left(2+\sqrt{x}\right)}{\sqrt{x}\left(\sqrt{x}-2\right).2\sqrt{x}\left(4+2\sqrt{x}\right)}\)
\(=\frac{\left(2+\sqrt{x}\right)}{\sqrt{x}\left(4+2\sqrt{x}\right)}=\frac{1}{2\sqrt{x}}\)
mk ko kt lại nên sai từ dòng 2 r, bạn cộng thêm (3+căn x) vào r giải tương tự
Rút gọn:
\(A=\left(\frac{4x\sqrt{x}+3x+9}{x+5\sqrt{x}+6}-\frac{3-\sqrt{x}}{2+\sqrt{x}}\right)\div\left(\frac{\sqrt{x}}{3+\sqrt{x}}-\frac{3+4\sqrt{x}}{x+5\sqrt{x}+6}\right)\)
\(B=\left(x-\sqrt{x}-2\right)\left(\dfrac{3}{\sqrt{x}-2}-\dfrac{4-\sqrt{x}}{x-2\sqrt{x}}\right)\)
cho bt \(P=(\frac{2\sqrt{x}-1}{2\sqrt{x}+1}-\frac{\sqrt{x}-4}{2x+3\sqrt{x}+1}).\left(\frac{2\sqrt{x}}{(2\sqrt{x}+1)\left(\sqrt{x}+1\right)}-\frac{3}{2\sqrt{x}+1}\right)\)
rút gọn P
stifm giá trị nhỏ nhất của P
cho bt A=
1.rút gọn A
2. Tìm x để a>2
\(\left(\frac{x}{x\sqrt{x}-4\sqrt{x}}-\frac{6}{3\sqrt{x}-6}+\frac{1}{\sqrt{x}+2}\right):\left(\sqrt{x}-2+\frac{10-x}{\sqrt{x}+2}\right)\)
1/ ĐKXĐ: \(\hept{\begin{cases}x>0\\x\ne4\end{cases}}\)
\(A=\left[\frac{x}{\sqrt{x}\left(x-4\right)}-\frac{6}{3\left(\sqrt{x}-2\right)}+\frac{1}{\sqrt{x}-2}\right]:\left(\frac{x-4+10-x}{\sqrt{x}+2}\right)\)
\(=\left[\frac{\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}-\frac{2}{\sqrt{x}-2}+\frac{1}{\sqrt{x}-2}\right]:\left(\frac{6}{\sqrt{x}+2}\right)\)
\(=\frac{\sqrt{x}-2\left(\sqrt{x}+2\right)+\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}.\frac{\left(\sqrt{x}+2\right)}{6}\)
\(=\frac{-2}{\sqrt{x}-2}.\frac{1}{6}=-\frac{1}{3\left(\sqrt{x}-2\right)}\)
2/ Để \(A>2\Rightarrow\frac{-1}{3\left(\sqrt{x}-2\right)}>2\)\(\Rightarrow6\sqrt{x}-12+1>0\Rightarrow6\sqrt{x}-11>0\Rightarrow\sqrt{x}>\frac{11}{6}\)
\(\Rightarrow x>\frac{121}{36}\)
rút gọn bt :
\(\left(\frac{8-x\sqrt{x}}{2-\sqrt{x}}+2\sqrt{x}\right)\left(\frac{2-\sqrt{x}}{2+\sqrt{X}}\right)^2\)
Rút gọn:
\(\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right):\frac{x-6\sqrt{x}+9}{\left(2-\sqrt{x}\right)\left(\sqrt{x}-3\right)}\)
= \(\left[\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right]:\frac{x-6\sqrt{x}+9}{\left(2-\sqrt{x}\right)\left(\sqrt{x}-3\right)}\)
= \(\left[\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}+\frac{4x}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\right]:\frac{\left(\sqrt{x}-3\right)^2}{\left(2-\sqrt{x}\right)\left(\sqrt{x}-3\right)}\)
= \(\left[\frac{\left(2+\sqrt{x}\right)^2}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}-\frac{\left(2-\sqrt{x}\right)^2}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}+\frac{4x}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\right]:\frac{\sqrt{x}-3}{2-\sqrt{x}}\)
= \(\left[\frac{4+4\sqrt{x}+x-4+4\sqrt{x}-x+4x}{nt}\right]:nt\)
\(=\left[\frac{8\sqrt{x}+4x}{nt}\right]:nt\)
\(=\left[\frac{4\sqrt{x}\left(2+\sqrt{x}\right)}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\right]:nt\)
\(=\frac{4\sqrt{x}}{2-\sqrt{x}}.\frac{\left(2-\sqrt{x}\right)}{\sqrt{x}-3}\)
\(=\frac{4\sqrt{x}}{\sqrt{x}-3}\)
rút gọn Bt
a)\(\frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}-\left(\sqrt{x}-\sqrt{y}\right)^2\)
b)\(\frac{x-y}{\sqrt{y}-1}.\sqrt{\frac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\left(x\ne1,y\ne1,y>0\right)\)
a) \(\frac{\left(\sqrt{x}\right)^3-\left(\sqrt{y}\right)^3}{\left(\sqrt{x}-\sqrt{y}\right)}-\left(\sqrt{x}-\sqrt{y}\right)^2=\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\sqrt{x}-\sqrt{y}}-x+2\sqrt{xy}-y\)
\(=3\sqrt{xy}\)
b) \(\frac{x-y}{\sqrt{y}-1}.\sqrt{\frac{\left(\sqrt{y}-1\right)^4}{\left(x-1\right)^4}}=\frac{x-y}{\sqrt{y}-1}.\frac{\left(\sqrt{y}-1\right)^2}{\left(x-1\right)^2}=\frac{\left(x-y\right)\left(\sqrt{y}-1\right)}{\left(x-1\right)^2}\)
a) \(=\frac{\left(\sqrt{x}\right)^3-\left(\sqrt{y}\right)^3}{\sqrt{x}-\sqrt{y}}-\left(\sqrt{x}-\sqrt{y}\right)^2=x+\sqrt{xy}+y-x+2\sqrt{xy}-y=3\sqrt{xy}\)
\(B=\left(\frac{\sqrt{x}}{x-4}+\frac{2}{2-\sqrt{x}}+\frac{1}{\sqrt{x}+2}\right):\left(\sqrt{x}-2+\frac{10-x}{\sqrt{x}+2}\right) \)
a, Rút gọn bt B
b tìm gt của x đẻ A>0
a) ta thấy x-4=(canx-2)(cãnx+2)
2-canx=-(cãnx - 2)
tự học mới giỏi
b)rut gọn roi giai cho