rút gọn
\(\left(1-\sqrt{x}\right).\left(1+\sqrt{x}+x\right)\)
Những câu hỏi liên quan
Rút gọn các biểu thức sau:
A 3left(x+2sqrt{x}right)-left(sqrt{x}-1right)left(sqrt{x}+1right)
B left(sqrt{x}+1right)left(sqrt{x}+3right)-2left(sqrt{x}-1right)^2
C 3x-3sqrt{x}-2+left(sqrt{x}-1right)left(sqrt{x}+1right)
D left(sqrt{x}+3right)left(sqrt{x}-3right)-left(2sqrt{x}+1right)left(sqrt{x}-2right)
E left(sqrt{x}+4right)left(sqrt{x}-4right)-left(2sqrt{x}-1right)left(sqrt{x}+2right)
Đọc tiếp
Rút gọn các biểu thức sau:
A= \(3\left(x+2\sqrt{x}\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
B= \(\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)-2\left(\sqrt{x}-1\right)^2\)
C= \(3x-3\sqrt{x}-2+\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
D= \(\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
E= \(\left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right)-\left(2\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)
\(A=3\left(x+2\sqrt{x}\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
\(=3x+6\sqrt{x}-\left(x-1\right)\)
\(=3x+6\sqrt{x}-x+1\)
\(=2x+6\sqrt{x}+1\)
\(B=\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)-2\left(\sqrt{x}-1\right)^2\)
\(=x+3\sqrt{x}+\sqrt{x}+3-2\left(x-2\sqrt{x}+1\right)\)
\(=x+4\sqrt{x}+3-2x+4\sqrt{x}-2\)
\(=-x+8\sqrt{x}+1\)
\(C=3x-3\sqrt{x}-2+\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
\(=3x-3\sqrt{x}-2+\left(\sqrt{x^2}-1\right)\)
\(=3x-3\sqrt{x}-2+x-1\)
\(=4x-3\sqrt{x}-3\)
\(D=\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
\(=x-9-\left(2x-3\sqrt{x}-2\right)\)
\(=x-9-2x+3\sqrt{x}+2\)
\(=-x+3\sqrt{x}-7\)
\(E=\left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right)-2\left(2\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)
\(=\sqrt{x^2}-2^2-2\left(2x+4\sqrt{x}-\sqrt{x}-2\right)\)
\(=x-4-2\left(2x+3\sqrt{x}-2\right)\)
\(=x-4-4x-6\sqrt{x}+4\)
\(=-3-6\sqrt{x}\)
Đúng 4
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Rút gọn :\(\frac{x}{\left(\sqrt{x}+\sqrt{y}\right).\left(1-\sqrt{y}\right)}-\frac{y}{\left(\sqrt{x}+\sqrt{y}\right).\left(\sqrt{x}+1\right)}-\frac{xy}{\left(\sqrt{x}+1\right).\left(1-\sqrt{y}\right)}\)
1) Rút gọn biểu thức
P=\(\left(\dfrac{2\sqrt{x}+x+1}{\sqrt{x}+1}\right).\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right):\left(1-\sqrt{x}\right)\)
Ta có: \(P=\left(\dfrac{2\sqrt{x}+x+1}{\sqrt{x}+1}\right)\cdot\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right):\left(1-\sqrt{x}\right)\)
\(=\left(\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}+1}\right)\cdot\left(1-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\right)\cdot\dfrac{1}{1-\sqrt{x}}\)
\(=\left(\sqrt{x}+1\right)\left(1-\sqrt{x}\right)\cdot\dfrac{1}{1-\sqrt{x}}\)
\(=\sqrt{x}+1\)
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Rút gọn: \(1-\left(\dfrac{2x-1+\sqrt{x}}{1-x}+\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{ }}x\right)\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)
\(P=\left(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\right):\left[\dfrac{2\left(x-2\sqrt{x}+1\right)}{x-1}\right]\)
Rút gọn
Ta có:
\(P=\left(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}\right):\left[\dfrac{2\left(x-2\sqrt{x}+1\right)}{x-1}\right]\\ =\left[\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\right]:\left[\dfrac{2\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]\\ =2:\dfrac{2\left(\sqrt{x}-1\right)}{\sqrt{x}+1}=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
Đúng 3
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P=\(\left(\dfrac{\sqrt{x^3}-1}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x^3}+1}{\sqrt{x}\left(\sqrt{x}+1\right)}\right):\left[\dfrac{2\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]\)
P=\(\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}:\left[\dfrac{2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)}\right]\)
P=\(\dfrac{x+\sqrt{x}+1}{\sqrt{x}}-\dfrac{x-\sqrt{x}+1}{\sqrt{x}}.\dfrac{\sqrt{x}+1}{2\left(\sqrt{x}-1\right)}\)
P=\(\dfrac{x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}.\dfrac{\sqrt{x}+1}{2\left(\sqrt{x}-1\right)}\)
P=\(\dfrac{2\sqrt{x}}{\sqrt{x}}.\dfrac{\sqrt{x}+1}{2\left(\sqrt{x}-1\right)}=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
Đúng 2
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Cho x>1 .Hãy rút gọn đa thức sau:
\(M=1-\left[\left(\dfrac{1}{\sqrt{x}-1}-\sqrt{x-1}\right):\left(\dfrac{1}{\sqrt{x+1}}-\dfrac{1}{\sqrt{x-1}}\right):\dfrac{\sqrt{x}+1.\sqrt{x^2-1}}{\left(x-1\right)\sqrt{x+1}-\left(x+1\right).\sqrt{x-1}}\right]\)
rút gọn bt sau: a=\(\left(\dfrac{x-1}{\sqrt{x}-1}+\dfrac{x\sqrt{x}-a}{1-x}\right):\left(\dfrac{\left(\sqrt{x}-1\right)^2+\sqrt{x}}{\sqrt{x}+1}\right)\)
Đoạn $x\sqrt{x}-a$ là sao vậy bạn? Có nhầm lẫn gì không?
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\(=\left(\sqrt{x}+1-\dfrac{x+\sqrt{x}+1}{\sqrt{x}+1}\right):\dfrac{x-\sqrt{x}+1}{\sqrt{x}+1}\)
\(=\dfrac{x+2\sqrt{x}+1-x-\sqrt{x}-1}{\sqrt{x}+1}\cdot\dfrac{\sqrt{x}+1}{x-\sqrt{x}+1}\)
\(=\dfrac{\sqrt{x}}{x-\sqrt{x}+1}\)
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\(\left(1+\dfrac{x+\sqrt{x}}{1+\sqrt{x}}\right).\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\) . Rút gọn
\(\left(1+\dfrac{x+\sqrt{x}}{1+\sqrt{x}}\right).\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\left(đk:x\ge0,x\ne1\right)\)
\(=\dfrac{1+\sqrt{x}+x+\sqrt{x}}{1+\sqrt{x}}.\dfrac{1-\sqrt{x}+x-\sqrt{x}}{1-\sqrt{x}}\)
\(=\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}+1}.\dfrac{\left(1-\sqrt{x}\right)^2}{1-\sqrt{x}}=\left(\sqrt{x}+1\right)\left(1-\sqrt{x}\right)=1-x\)
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\(\left(1+\dfrac{x+\sqrt{x}}{1+\sqrt{x}}\right).\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\\ =\left(1+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{1+\sqrt{x}}\right).\left(1+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{1-\sqrt{x}}\right)\\ =\left(1+\sqrt{x}\right).\left(1-\sqrt{x}\right)\\ =1-x\)
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\(\left(1+\dfrac{x+\sqrt{x}}{1+\sqrt{x}}\right).\left(1+\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\right)\)
\(=\left(1+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}\right).\left(1-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\right)\)
\(=\left(1+\sqrt{x}\right)\left(1-\sqrt{x}\right)=1+\sqrt{x}-\sqrt{x}-x=1-x\)
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Xem thêm câu trả lời
14 tháng 8 2021 lúc 10:24
Rút gọn:
\(A=\left(\dfrac{2x-1+\sqrt{x}}{1-x}+\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x+\sqrt{x}}\right).\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}-1\)
25 tháng 6 2021 lúc 10:29
\(\dfrac{x-2\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
rút gọn
Hình như sai đề :_:
*Sửa lại:
`(x-2sqrtx+1)/((sqrtx-1)(sqrtx+1))`
`=(sqrtx-1)^2/((sqrtx-1)(sqrtx+1))`
`=(sqrtx-1)/(sqrtx+1)`
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Sửa đề: \(\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
Ta có: \(\dfrac{x-2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}\)
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