\(\left(\frac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\cdot\frac{1+2\sqrt{a}+a}{\left(1-a\right)^2}+\sqrt{a}\) (a≥0; a≠ -1)
a ) rút gọn
Những câu hỏi liên quan
Rút gọn biểu thức:
1) Pfrac{x^2-sqrt{x}}{x+sqrt{x}+1}-frac{2x+sqrt{x}}{sqrt{x}}+frac{2cdotleft(x-1right)}{sqrt{x}-1}
2) Pleft(frac{sqrt{x}-2}{sqrt{x}-1}-frac{sqrt{x}+2}{x+2sqrt{x}+1}right)cdotfrac{left(1-xright)^2}{2}
3) Bleft(frac{1-asqrt{a}}{1-sqrt{a}}+sqrt{a}right)cdotleft(frac{1+asqrt{a}}{1+sqrt{a}}-sqrt{a}right)
4) Kleft(frac{sqrt{a}}{sqrt{a}-1}-frac{1}{a-sqrt{a}}right)divleft(frac{1}{sqrt{a}+1}-frac{2}{a-1}right)
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Rút gọn biểu thức:
1) \(P=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\cdot\left(x-1\right)}{\sqrt{x}-1}\)
2) \(P=\left(\frac{\sqrt{x}-2}{\sqrt{x}-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\cdot\frac{\left(1-x\right)^2}{2}\)
3) \(B=\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\cdot\left(\frac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\)
4) \(K=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right)\div\left(\frac{1}{\sqrt{a}+1}-\frac{2}{a-1}\right)\)
\(B=\left(\frac{6}{a-1}+\frac{10-2\sqrt{a}}{a\sqrt{a}-a-\sqrt{a}+1}\right)\cdot\frac{\left(\sqrt{a}-1\right)^2}{4\sqrt{a}}\) (với a>0;a≠1)
Đặt \(C=B\cdot\left(a-\sqrt{a}+1\right)\) . So sánh C và 1
uses crt;
var B,C: real;
a:real;
begin
clrscr;
writeln('a = '); read(a);
B:=(6/(a-1)+(10-2*sqrt(a))/(a*sqrt(a)-a-sqrt(a)+1))*(((sqrt(a)-1)*(sqrt(a)-1))/(4*sqrt(a)));
C:=B*(a-sqrt(a)+1);
if C > 1 then writeln('C > 1');
if C < 1 then writeln('C < 1');
if C = 1 then writeln('C = 1');
readln
end.
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\(\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{2}{a-4}\right)\cdot\left(\sqrt{a}-1+\frac{\sqrt{a}-4}{\sqrt{a}}\right)\)
=\(\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\right).\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}}+\frac{\sqrt{a}-4}{\sqrt{a}}\right)\) =\(\left(\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}-\frac{2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\right).\left(\frac{a-\sqrt{a}+\sqrt{a}-4}{\sqrt{a}}\right)\) =\(\left(\frac{a+2\sqrt{a}+\sqrt{a}+2-2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\right).\left(\frac{a-4}{\sqrt{a}}\right)\)=\(\frac{a+3\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}.\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\sqrt{a}}\) =\(\frac{\sqrt{a}\left(\sqrt{a}+3\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}.\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\sqrt{a}}\) =\(\sqrt{a}+3\)
Cho \(A=\left(\frac{\sqrt{a}}{2}-\frac{1}{2 \sqrt{a}}\right)^{2} \cdot\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)
a) Rút gọn A
b) Tìm a để A<0
c) Tìm a để A=-2
Cho \(A=\left(\frac{\sqrt{a}}{2}-\frac{1}{2 \sqrt{a}}\right)^{2} \cdot\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)
a) Rút gọn A
b) Tìm a để A<0
c) Tìm a để A=-2
C/m biểu thứca)left(frac{asqrt{a}+bsqrt{b}}{sqrt{a}+sqrt{b}}-sqrt{ab}right)left(frac{sqrt{a}+sqrt{b}}{a-b}right)1(a,b0,ane0b)frac{a-b-2sqrt{ab}}{sqrt{a}-sqrt{b}}:frac{1}{sqrt{a}+sqrt{b}}a-bleft(a,b0,ane bright)c)left(2+frac{a-sqrt{a}}{sqrt{a}-1}right)left(2-frac{a+sqrt{a}}{sqrt{a}+1}right)4-aleft(a0,ane1right)d)left(frac{1-asqrt{a}}{1-sqrt{a}}+sqrt{a}right)left(frac{1+asqrt{a}}{1+sqrt{a}}-sqrt{a}right)left(1-aright)^2left(age0,ane1right)Giải giúp mk với. THứ 3 tuần sau là phải nộp rồi
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C/m biểu thức
a)\(\left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\left(\frac{\sqrt{a}+\sqrt{b}}{a-b}\right)=1\)(a,b>0,a\(\ne\)0
b)\(\frac{a-b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}:\frac{1}{\sqrt{a}+\sqrt{b}}=a-b\left(a,b>0,a\ne b\right)\)
c)\(\left(2+\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(2-\frac{a+\sqrt{a}}{\sqrt{a}+1}\right)=4-a\left(a>0,a\ne1\right)\)
d)\(\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)=\left(1-a\right)^2\left(a\ge0,a\ne1\right)\)
Giải giúp mk với. THứ 3 tuần sau là phải nộp rồi
\(\left(\frac{\sqrt{a}-2}{a-1}-\frac{\sqrt{a}+2}{a+2\sqrt{a}+1}\right)\cdot\frac{\left(1-a\right)^2}{2}\)
Rút gọn biểu thức:
\(P=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\cdot\left(x-1\right)}{\sqrt{x}-1}\)
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right)\div\left(\frac{1}{\sqrt{a}+1}-\frac{2}{a-1}\right)\)
ĐKXĐ: Bạn tự làm nha
\(P=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\left(x-1\right)}{\sqrt{x}-1}\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{\sqrt{x}\left(2\sqrt{x}+1\right)}{\sqrt{x}}+\frac{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\left(2\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-2\sqrt{x}-1+2\sqrt{x}+2\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}+1\)
\(=\frac{x^2-\sqrt{x}+x+\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\frac{x^2+x+1}{x+\sqrt{x}+1}\)
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}-\frac{2}{a-1}\right)\)
\(=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\left(\frac{1}{\sqrt{a}+1}-\frac{2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\)
\(=\frac{a-1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{1\left(\sqrt{a}-1\right)-2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\)
\(=\frac{\left(\sqrt{a}+1\right)}{\sqrt{a}}.\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\sqrt{a}-1-2}\)
\(=\frac{\left(\sqrt{a}+1\right)\left(a-1\right)}{\sqrt{a}\left(\sqrt{a}-3\right)}\)
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Cho P=\(\left(\frac{\sqrt{a}}{2}-\frac{1}{a\sqrt{a}}\right)\cdot\left(\frac{a-\sqrt{a}}{\sqrt{a}+1}-\frac{a+\sqrt{a}}{\sqrt{a}-1}\right)\) với a>0, a khác 1
a, Rút gọn P
b, Tìm a để P> hoặc bằng 2
Mong mn giúp mk cần gấp nha!!