\(B=\frac{3\sqrt{x}+4}{3\sqrt{x}-2}-\frac{42\sqrt{x}+34}{15x+11\sqrt{x}-14}\)
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Bài 8 : Cho biểu thức P = \(\frac{3-\sqrt{x}}{5\sqrt{x}+7}+\frac{3\sqrt{x}+4}{3\sqrt{x}-2}-\frac{42\sqrt{x}+34}{15+11\sqrt{x}-14}\)
a) đkxđ và rút gọn
b) tìm x để P\(\le\)\(\frac{-2}{3}\)
c) tìm x để P nguyên
Q= \(\dfrac{3-\sqrt{x}}{5\sqrt{x}+7}+\dfrac{3\sqrt{x}+4}{3\sqrt{x}-2}-\dfrac{42\sqrt{x}+34}{15x+11\sqrt{x}-14}\)
a, Rút gọn
b, Tìm x sao cho Q ≤-\(\dfrac{2}{3}\)
c, Tìm các giá trị nguyên của x sao cho Q nhận giá trị nguyên
a: \(Q=\dfrac{9\sqrt{x}-6-3x+2\sqrt{x}+15x+41\sqrt{x}+28-42\sqrt{x}-34}{\left(5\sqrt{x}+7\right)\left(3\sqrt{x}-2\right)}\)
\(=\dfrac{12x+10\sqrt{x}-12}{\left(5\sqrt{x}+7\right)\left(3\sqrt{x}-2\right)}\)
\(=\dfrac{12x+18\sqrt{x}-8\sqrt{x}-12}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}\)
\(=\dfrac{6\sqrt{x}\left(2\sqrt{x}+3\right)-4\left(2\sqrt{x}+3\right)}{\left(3\sqrt{x}-2\right)\left(5\sqrt{x}+7\right)}\)
\(=\dfrac{4\sqrt{x}+6}{5\sqrt{x}+7}\)
c: Để Q là số nguyên thì \(20\sqrt{x}+30⋮5\sqrt{x}+7\)
\(\Leftrightarrow5\sqrt{x}+7\inƯ\left(2\right)\)
hay \(x\in\varnothing\)
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a)sqrt{x^2+2x+10}+x^2+2x+80
b)15x-2x^2-5sqrt{2x^2-15x+11}
c)sqrt{9x^2+45}+sqrt{16x^2+80}+3sqrt{frac{x^2+5}{16}}-frac{1}{4}sqrt{frac{25x^2+15}{9}}9
d)3x^2+21x+18+2sqrt{x^2+7x+7}2
e)sqrt{x^2+3x+2}-2sqrt{2x^2+6x+2}-sqrt{2}
f)sqrt{x-1}+sqrt{x+3}-sqrt{x^2+2x-3}-10
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a)\(\sqrt{x^2+2x+10}+x^2+2x+8=0\)
b)\(15x-2x^2-5=\sqrt{2x^2-15x+11}\)
c)\(\sqrt{9x^2+45}+\sqrt{16x^2+80}+3\sqrt{\frac{x^2+5}{16}}-\frac{1}{4}\sqrt{\frac{25x^2+15}{9}}=9\)
d)\(3x^2+21x+18+2\sqrt{x^2+7x+7}=2\)
e)\(\sqrt{x^2+3x+2}-2\sqrt{2x^2+6x+2}=-\sqrt{2}\)
f)\(\sqrt{x-1}+\sqrt{x+3}-\sqrt{x^2+2x-3}-1=0\)
a) + \(VT=\sqrt{x^2+2x+10}+x^2+2x+1+7\)
\(=\sqrt{x^2+2x+1}+\left(x+1\right)^2+7>0\forall x\)
=> ptvn
d) ĐK : \(x^2+7x+7\ge0\)
Đặt \(t=\sqrt{x^2+7x+7}\ge0\) \(\Rightarrow t^2=x^2+7x+7\)
\(pt\Leftrightarrow3\left(x^2+7x+7\right)-3+2\sqrt{x^2+7x+7}-2=0\)
\(\Leftrightarrow3t^2+2t-5=0\Leftrightarrow\left(3t+5\right)\left(t-1\right)=0\)
\(\Leftrightarrow t=1\) ( do \(3t+5>0\forall t\ge0\) )
\(\Leftrightarrow x^2+7x+1=0\Leftrightarrow x^2+7x+6=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+6\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-6\end{matrix}\right.\) ( TM )
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f) ĐK : \(x\ge1\)
Đặt \(\left\{{}\begin{matrix}a=\sqrt{x-1}\ge0\\b=\sqrt{x+3}\ge0\end{matrix}\right.\) thì pt trở thành :
\(a+b-ab-1=0\)
\(\Leftrightarrow\left(a-1\right)-b\left(a-1\right)=0\)
\(\Leftrightarrow\left(1-b\right)\left(a-1\right)=0\Leftrightarrow\left[{}\begin{matrix}a=1\\b=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}=1\\\sqrt{x+3}=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(TM\right)\\x=-2\left(KTM\right)\end{matrix}\right.\)
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bài 1) rút gọn
1) 5√frac{1}{5} 2)frac{12}{5}√frac{5}{4} 3)frac{30}{5sqrt{6}} 4) frac{20}{2sqrt{5}} 5)frac{2-sqrt{2}}{sqrt{2}} 6) frac{11+sqrt{11}}{1+sqrt{ }11} 7) frac{sqrt{21-sqrt{7}}}{1-sqrt{3}} 8)frac{sqrt{2+sqrt{3}}}{2+sqrt{6}} 9)frac{sqrt{10-sqrt{2}}}{sqrt{5-}1} 10)frac{2sqrt{3}-3sqrt{2}}{sqrt{3}-sqrt[]{2}}
bài 2) với các biểu thức đã cho là có nghĩa và rút gọn
1)frac{x-sqrt{x}}{sqrt{x}-1} 2)frac{xsqrt{x}-2x}{2-sqrt{x}} 3) frac{xsqrt{y}-...
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bài 1) rút gọn
1) 5√\(\frac{1}{5}\) 2)\(\frac{12}{5}\)√\(\frac{5}{4}\) 3)\(\frac{30}{5\sqrt{6}}\) 4) \(\frac{20}{2\sqrt{5}}\) 5)\(\frac{2-\sqrt{2}}{\sqrt{2}}\) 6) \(\frac{11+\sqrt{11}}{1+\sqrt{ }11}\) 7) \(\frac{\sqrt{21-\sqrt{7}}}{1-\sqrt{3}}\) 8)\(\frac{\sqrt{2+\sqrt{3}}}{2+\sqrt{6}}\) 9)\(\frac{\sqrt{10-\sqrt{2}}}{\sqrt{5-}1}\) 10)\(\frac{2\sqrt{3}-3\sqrt{2}}{\sqrt{3}-\sqrt[]{2}}\)
bài 2) với các biểu thức đã cho là có nghĩa và rút gọn
1)\(\frac{x-\sqrt{x}}{\sqrt{x}-1}\) 2)\(\frac{x\sqrt{x}-2x}{2-\sqrt{x}}\) 3) \(\frac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\) 4) \(\frac{a\sqrt{b}-\sqrt{a}}{\sqrt{b}-b\sqrt{a}}\) 5) \(\frac{a-1}{\sqrt{a}+1}\) 6) \(\frac{4-x}{2\sqrt{x}-x}\) 7)\(\frac{a+1+2\sqrt{a}}{1+\sqrt{a}}\) 8)\(\frac{3\sqrt{x}-x}{3+2\sqrt{3x}-x}\) 9)\(\frac{y+12-4\sqrt{3y}}{y-12}\) 10)\(\frac{4\sqrt{x}-x-4}{x-4}\) 11)\(\frac{x+y-2\sqrt{xy}}{x\sqrt{y}-y\sqrt{x}}\)
K=\(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(K=\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(=\frac{15\sqrt{x}-11}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{3\sqrt{x}}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(=\frac{15\sqrt{x}-11}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{3x+9\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{\left(2\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{15\sqrt{x}-11-3x-9\sqrt{x}-2x-\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
\(=\frac{-5x-5\sqrt{x}-8}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)
Kết quả số xấu thì không biết có sai dấu chỗ nào không
A= \(\frac{\sqrt{x}}{\sqrt{x}-2}\)+\(\frac{5}{\sqrt{x}+2}\)-\(\frac{11\sqrt{x}-14}{x-4}\)
a) rút gọn A
b) tìm x để A<\(\frac{-2}{3}\)
Tính
3) \(\frac{\sqrt{x}-1}{\sqrt{x}+1}+\frac{2x-\sqrt{x}-1}{x-\sqrt{x}+1}-\frac{3x\sqrt{x}-2x+\sqrt{x}-3}{x\sqrt{x}+1}\)
4) \(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
5)\(\frac{\sqrt{x}-1}{\sqrt{x}-3}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{x+5}{x-5\sqrt{x}+6}\)
Help !!! Mk đang cần gấp ,thank các ben
tính giá trị biểu thức
1) A frac{15sqrt{x}-11}{x-2sqrt{x}-3}+frac{3sqrt{x}-2}{1-sqrt{x}}-frac{2sqrt{x}+3}{sqrt{x}+3} tại x3-2sqrt{2}
2) Bfrac{x+2}{xsqrt{x}-1}+frac{sqrt{x}+1}{x+sqrt{x}+1}-frac{sqrt{x}+1}{x-1} tại x7-2sqrt{6}
3) Cleft(frac{sqrt{x}}{3+sqrt{x}}+frac{x+9}{9-x}right):left(frac{3sqrt{x}+1}{x-3sqrt{x}}-frac{1}{sqrt{x}}right) tại x7-4sqrt{3}
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tính giá trị biểu thức
1) A = \(\frac{15\sqrt{x}-11}{x-2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\) tại \(x=3-2\sqrt{2}\)
2) \(B=\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\) tại \(x=7-2\sqrt{6}\)
3) \(C=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{x+9}{9-x}\right):\left(\frac{3\sqrt{x}+1}{x-3\sqrt{x}}-\frac{1}{\sqrt{x}}\right)\) tại \(x=7-4\sqrt{3}\)
1) Sửa đề: \(A=\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
Ta có: \(A=\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)
\(=\frac{15\sqrt{x}-11}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{\left(3\sqrt{x}-2\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{\left(2\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{15\sqrt{x}-11-\left(3x+7\sqrt{x}-6\right)-\left(2x+\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{15\sqrt{x}-11-3x-7\sqrt{x}+6-2x-\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{-5x+7\sqrt{x}-2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{-5x+5\sqrt{x}+2\sqrt{x}-2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{-5\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{\left(\sqrt{x}-1\right)\left(-5\sqrt{x}+2\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\frac{-5\sqrt{x}+2}{\sqrt{x}+3}\)
Ta có: \(x=3-2\sqrt{2}\)
\(=2-2\cdot\sqrt{2}\cdot1+1\)
\(=\left(\sqrt{2}-1\right)^2\)
Thay \(x=\left(\sqrt{2}-1\right)^2\) vào biểu thức \(A=\frac{-5\sqrt{x}+2}{\sqrt{x}+3}\), ta được:
\(A=\frac{-5\cdot\sqrt{\left(\sqrt{2}-1\right)^2}+2}{\sqrt{\left(\sqrt{2}-1\right)^2}+3}\)
\(=\frac{-5\cdot\left(\sqrt{2}-1\right)+2}{\sqrt{2}-1+3}\)
\(=\frac{-5\sqrt{2}+5+2}{\sqrt{2}+2}\)
\(=\frac{-5\sqrt{2}+7}{\sqrt{2}+2}\)
Vậy: Khi \(x=3-2\sqrt{2}\) thì \(A=\frac{-5\sqrt{2}+7}{\sqrt{2}+2}\)
2) Ta có: \(B=\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\)
\(=\frac{\left(x+2\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(x+\sqrt{x}+1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{x\sqrt{x}+x+2\sqrt{x}+2+x+x\sqrt{x}-\sqrt{x}-1-\left(2x+2\sqrt{x}+x\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{2x+2x\sqrt{x}+\sqrt{x}+1-2x-2\sqrt{x}-x\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{x\sqrt{x}-\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{\sqrt{x}\left(x-1\right)}{\left(x-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{\sqrt{x}}{x+\sqrt{x}+1}\)
Ta có: \(x=7-2\sqrt{6}\)
\(=6-2\sqrt{6}\cdot1+1\)
\(=\left(\sqrt{6}-1\right)^2\)
Thay \(x=\left(\sqrt{6}-1\right)^2\) vào biểu thức \(B=\frac{\sqrt{x}}{x+\sqrt{x}+1}\), ta được:
\(B=\frac{\sqrt{\left(\sqrt{6}-1\right)^2}}{\left(\sqrt{6}-1\right)^2+\sqrt{\left(\sqrt{6}-1\right)^2}+1}\)
\(=\frac{\sqrt{6}-1}{7-2\sqrt{6}+\sqrt{6}-1+1}\)
\(=\frac{\sqrt{6}-1}{7-\sqrt{6}}\)
Vậy: Khi \(x=7-2\sqrt{6}\) thì \(B=\frac{\sqrt{6}-1}{7-\sqrt{6}}\)
3) Ta có: \(C=\left(\frac{\sqrt{x}}{3+\sqrt{x}}+\frac{x+9}{9-x}\right):\left(\frac{3\sqrt{x}+1}{x-3\sqrt{x}}-\frac{1}{\sqrt{x}}\right)\)
\(=\left(\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\frac{x+9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right):\left(\frac{3\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}-3}{\sqrt{x}\left(\sqrt{x}-3\right)}\right)\)
\(=\frac{x-3\sqrt{x}-x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}:\frac{3\sqrt{x}+1-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-3\right)}\)
\(=\frac{x-3\sqrt{x}-x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\cdot\frac{\sqrt{x}\left(\sqrt{x}-3\right)}{2\sqrt{x}+4}\)
\(=\frac{\sqrt{x}\left(x-3\sqrt{x}-x-9\right)}{\left(\sqrt{x}+3\right)\left(2\sqrt{x}+4\right)}\)
\(=\frac{\sqrt{x}\left(-3\sqrt{x}-9\right)}{\left(\sqrt{x}+3\right)\cdot2\cdot\left(\sqrt{x}+2\right)}\)
\(=\frac{-3\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(2\sqrt{x}+4\right)}\)
\(=\frac{-3\sqrt{x}}{2\sqrt{x}+4}\)
Ta có: \(x=7-4\sqrt{3}\)
\(=4-2\cdot2\cdot\sqrt{3}+3\)
\(=\left(2-\sqrt{3}\right)^2\)
Thay \(x=\left(2-\sqrt{3}\right)^2\) vào biểu thức \(C=\frac{-3\sqrt{x}}{2\sqrt{x}+4}\), ta được:
\(C=\frac{-3\cdot\sqrt{\left(2-\sqrt{3}\right)^2}}{2\cdot\sqrt{\left(2-\sqrt{3}\right)^2}+4}\)
\(=\frac{-3\cdot\left(2-\sqrt{3}\right)}{2\cdot\left(2-\sqrt{3}\right)+4}\)
\(=\frac{-6+3\sqrt{3}}{4-2\sqrt{3}+4}\)
\(=\frac{-6+3\sqrt{3}}{8-2\sqrt{3}}\)
Vậy: Khi \(x=7-4\sqrt{3}\) thì \(C=\frac{-6+3\sqrt{3}}{8-2\sqrt{3}}\)
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35Cho biểu thứcPleft[left(frac{1}{sqrt{x}}+frac{1}{sqrt{y}}right)frac{2}{sqrt{x}+sqrt{y}}+frac{1}{x}+frac{1}{y}right]:frac{sqrt{x^3}+ysqrt{x}+xsqrt{y}+sqrt{y^3}}{sqrt{xy^3}+sqrt{x^3y}}a) Rút gọn Pb)Cho xy16 . Tìm Min P 34 Cho biểu thức Pfrac{x}{sqrt{xy}-2y}-frac{2sqrt{x}}{x+sqrt{x}-2sqrt{xy}-2sqrt{y}}-frac{1-x}{1-sqrt{x}}a) Rút gọn Pb)Tính P biết 2x^2+y^2-4x-2xy+40
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35Cho biểu thức
P=\(\left[\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right)\frac{2}{\sqrt{x}+\sqrt{y}}+\frac{1}{x}+\frac{1}{y}\right]:\frac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{xy^3}+\sqrt{x^3y}}\)
a) Rút gọn P
b)Cho xy=16 . Tìm Min P
34 Cho biểu thức
P=\(\frac{x}{\sqrt{xy}-2y}-\frac{2\sqrt{x}}{x+\sqrt{x}-2\sqrt{xy}-2\sqrt{y}}-\frac{1-x}{1-\sqrt{x}}\)
a) Rút gọn P
b)Tính P biết 2x^2+y^2-4x-2xy+4=0