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\(A=\dfrac{-\left(\sqrt{x}+1\right)\left(2+\sqrt{x}\right)-2\sqrt{x}\left(2-\sqrt{x}\right)+5\sqrt{x}+2}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}:\dfrac{\sqrt{x}\left(3-\sqrt{x}\right)}{\left(\sqrt{x}+2\right)^2}\)
\(A=\dfrac{-3\sqrt{x}-x-2-4\sqrt{x}+2x+5\sqrt{x}+2}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}.\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}\left(3-\sqrt{x}\right)}\)
\(A=\dfrac{-x-2\sqrt{x}}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}.\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}\left(3-\sqrt{x}\right)}\)
\(A=\dfrac{-\sqrt{x}\left(\sqrt{x}+2\right)^3}{\left(\sqrt{x}+2\right)\left(2-\sqrt{x}\right)\sqrt{x}\left(3-\sqrt{x}\right)}=\dfrac{-\left(\sqrt{x}+2\right)^2}{\left(2-\sqrt{x}\right)\left(3-\sqrt{x}\right)}\)
\(P=\dfrac{\sqrt{2}\left(3+\sqrt{5}\right)}{\sqrt{2}\left(2\sqrt{2}+\sqrt{3+\sqrt{5}}\right)}+\dfrac{\sqrt{2}\left(3-\sqrt{5}\right)}{\sqrt{2}\left(2\sqrt{2}-\sqrt{3-\sqrt{5}}\right)}\)
\(=\dfrac{3\sqrt{2}+\sqrt{10}}{4+\sqrt{6+2\sqrt{5}}}+\dfrac{3\sqrt{2}-\sqrt{10}}{4-\sqrt{6-2\sqrt{5}}}\)
\(=\dfrac{3\sqrt{2}+\sqrt{10}}{5+\sqrt{5}}+\dfrac{3\sqrt{2}-\sqrt{10}}{5-\sqrt{5}}\)
\(=\dfrac{\left(3\sqrt{2}+\sqrt{10}\right)\left(5-\sqrt{5}\right)+\left(3\sqrt{2}-\sqrt{10}\right)\left(5+\sqrt{5}\right)}{20}\)
\(=\dfrac{15\sqrt{2}-3\sqrt{10}+5\sqrt{10}-5\sqrt{2}+15\sqrt{2}+3\sqrt{10}-5\sqrt{10}-5\sqrt{2}}{20}\)
\(=\dfrac{30\sqrt{2}-10\sqrt{2}}{20}=\dfrac{20\sqrt{2}}{20}=\sqrt{2}\)
\(\)
bài 1 rút gon biểu thức
\(6\sqrt{\dfrac{2}{3}}-\sqrt{24}+2\sqrt{\dfrac{3}{8}}+2\sqrt{\dfrac{1}{6}}\)
`6\sqrt(2/3)-\sqrt(24)+2\sqrt(3/8)+2\sqrt(1/6)`
`=6. \sqrt6/3 - \sqrt(2^2 .6) + 2. \sqrt(24)/8 + 2. \sqrt6/6`
`=2\sqrt6-2\sqrt6+ \sqrt6/2 + \sqrt6/3`
`=\sqrt6/2+\sqrt6/3`
`=(3\sqrt6+2\sqrt6)/6`
`=(5\sqrt6)/6`
Ta có: \(6\sqrt{\dfrac{2}{3}}-\sqrt{24}+2\sqrt{\dfrac{3}{8}}+2\sqrt{\dfrac{1}{6}}\)
\(=\dfrac{6\sqrt{2}}{\sqrt{3}}-2\sqrt{6}+2\cdot\dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{2}{\sqrt{6}}\)
\(=2\sqrt{6}-2\sqrt{6}+\dfrac{\sqrt{3}}{\sqrt{2}}+\dfrac{\sqrt{2}}{\sqrt{3}}\)
\(=\dfrac{\sqrt{6}}{2}+\dfrac{\sqrt{6}}{3}=\dfrac{5\sqrt{6}}{6}\)
Bài 1:
Gọi biểu thức trên là $P$
\(P=\frac{\sqrt{x}(\sqrt{x}-3)+3(\sqrt{x}+3)}{(\sqrt{x}+3)(\sqrt{x}-3)}.\frac{x-9}{\sqrt{x}-3}\)
\(=\frac{x+9}{(\sqrt{x}-3)(\sqrt{x}+3)}.\frac{(\sqrt{x}-3)(\sqrt{x}+3)}{\sqrt{x}-3}=\frac{x+9}{\sqrt{x}-3}\)
Bài 2:
Để $(d)$ và $(d')$ song song với nhau thì:
$m^2-3=2m$
$\Leftrightarrow m^2-2m-3=0$
$\Leftrightarrow (m+1)(m-3)=0$
$\Leftrightarrow m+1=0$ hoặc $m-3=0$
$\Leftrightarrow m=-1$ hoặc $m=3$
\(ĐKXĐ:x\ge0,x\ne1\)
= \(\dfrac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
= \(\dfrac{x+2+\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
= \(\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\) (1)
b/ Ta có: \(x=4-2\sqrt{3}=3-2\sqrt{3}+1=\left(\sqrt{3}-1\right)^2\)
Thay \(x=\left(\sqrt{3}-1\right)^2\) vào (1) ta được:
\(\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\left(\sqrt{3}-1\right)^2+\sqrt{\left(\sqrt{3}-1\right)^2}+1}\)= \(\dfrac{\sqrt{3}-1}{4-2\sqrt{3}+\sqrt{3}-1+1}=\dfrac{\sqrt{3}-1}{4-\sqrt{3}}\) = \(\dfrac{\left(\sqrt{3}-1\right)\left(4+\sqrt{3}\right)}{\left(4-\sqrt{3}\right)\left(4+\sqrt{3}\right)}=\dfrac{3\sqrt{3}-1}{13}\)
Vậy giá trị của A khi \(x=4-2\sqrt{3}\) là \(\dfrac{3\sqrt{3}-1}{13}\)
\(p=\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
\(=\dfrac{x+2}{\left(x-1\right)\left(x+\sqrt{x}+1\right)}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
=\(\dfrac{x-\sqrt{x}}{x\sqrt{x}-1}\)
=\(\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
=\(\dfrac{\sqrt{x}}{x+\sqrt{x}+1}\)
học tốt nhé anh trai
\(P=\dfrac{\left(\sqrt{a+1}+1\right)\left(\sqrt{a+1}+2\right)}{\left(\sqrt{a+1}-2\right)\left(\sqrt{a+1}+2\right)}+\dfrac{2\sqrt{a+1}\left(\sqrt{a+1}-2\right)}{\left(\sqrt{a+1}-2\right)\left(\sqrt{a+1}+2\right)}-\dfrac{2+5\sqrt{a+1}}{a-3}\)
\(P=\dfrac{a+3+3\sqrt{a+1}}{a-3}+\dfrac{2a+2-4\sqrt{a+1}}{a-3}-\dfrac{2+5\sqrt{a+1}}{a-3}\)
\(P=\dfrac{a+3+3\sqrt{a+1}+2a+2-4\sqrt{a+1}-2-5\sqrt{a+1}}{a-3}\)
\(P=\dfrac{3a+3-6\sqrt{a+1}}{a-3}\)
Có thể dừng ở đây hoặc nếu thích thì làm tiếp như sau (chưa chắc gọn hơn):
\(P=\dfrac{3\left(a+1\right)-6\sqrt{a+1}}{\left(\sqrt{a+1}-2\right)\left(\sqrt{a+1}+2\right)}=\dfrac{3\sqrt{a+1}\left(\sqrt{a+1}-2\right)}{\left(\sqrt{a+1}-2\right)\left(\sqrt{a+1}+2\right)}\)
\(P=\dfrac{3\sqrt{a+1}}{\sqrt{a+1}-2}\)
\(=\dfrac{\sqrt{3}+1}{2\sqrt{2}}:\left(\dfrac{\sqrt{3}+1}{2\sqrt{2}}-\dfrac{2}{\sqrt{6}}+\dfrac{\sqrt{3}+1}{2\sqrt{6}}\right)\)
\(=\dfrac{\sqrt{3}+1}{2\sqrt{2}}:\left(\dfrac{3+\sqrt{3}}{2\sqrt{6}}-\dfrac{4}{2\sqrt{6}}+\dfrac{\sqrt{3}+1}{2\sqrt{6}}\right)\)
\(=\dfrac{\sqrt{3}+1}{2\sqrt{2}}\cdot\dfrac{2\sqrt{6}}{3+\sqrt{3}-4+\sqrt{3}+1}\)
\(=\sqrt{3}\cdot\dfrac{\sqrt{3}+1}{2\sqrt{3}}=\dfrac{\sqrt{3}+1}{2}\)
\(=\left(\sqrt{x}+\sqrt{x-1}-\sqrt{x-1}+\sqrt{2}\right)\cdot\left(\dfrac{2\sqrt{x}-\sqrt{x}-\sqrt{2}}{\sqrt{x}\left(2-\sqrt{x}\right)}\right)\)
\(=\dfrac{\left(\sqrt{x}+\sqrt{2}\right)}{-\sqrt{x}}\)
a: \(=\dfrac{6+4\sqrt{2}}{\sqrt{2}+2+\sqrt{2}}+\dfrac{6-4\sqrt{2}}{\sqrt{2}-2+\sqrt{2}}\)
\(=\dfrac{6+4\sqrt{2}}{2+2\sqrt{2}}+\dfrac{6-4\sqrt{2}}{2\sqrt{2}-2}\)
\(=\dfrac{3+2\sqrt{2}}{\sqrt{2}+1}+\dfrac{3-2\sqrt{2}}{\sqrt{2}-1}\)
=căn 2+1+căn 2-1=2căn 2
b: \(=\dfrac{\sqrt{3}+\sqrt{3+\sqrt{3}}+\sqrt{3}-\sqrt{3+\sqrt{3}}}{1-\sqrt{3}-1}=\dfrac{-2\sqrt{3}}{\sqrt{3}}=-2\)
bạn ơi cho mình hỏi câu b chi tiết hơn đước ko ạ
mình chưa hiểu lắm
Đặt \(\sqrt[3]{2}=a\)
\(A+\dfrac{a+a^2+a^3}{a^2+a+1}=\dfrac{a\left(a^2+a+1\right)}{a^2+a+1}=a=\sqrt[3]{2}\)