a, \(\frac{132639}{173451}\) b, \(\frac{16515}{20919}\)
Những câu hỏi liên quan
( * là nhân còn / là phần)
Rút gọn:
A= 132639/173451
B= 16515/20919
C= 11*12+22*24+44*48/33*36+66*72+132*144
( CÁC BẠN TRÌNH BÀY ĐẦY ĐỦ HỘ MÌNH NHÉ)
\(A=\frac{132639}{173451}\)
\(A=\frac{132639:10203}{173451:10203}\)
\(A=\frac{13}{17}\)
\(B=\frac{16515}{20919}\)
\(B=\frac{16515:1101}{20919:1101}\)
\(B=\frac{15}{19}\)
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1,Rút gọn phân số
a, 123639/173451 b,16515/20919 c, C= 11.12+22.24+44.48/33.36+66.72+132.144
\(\frac{a}{\sqrt{ab}+b}+\frac{b}{\sqrt{ab}+a}-\frac{a+b}{\sqrt{ab}}\)
rut gon
A=\(\frac{a\sqrt{a}+b\sqrt{b}-\left(a+b\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}\)=\(\frac{-a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}\)=\(\frac{-\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}\)=\(-1\)
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rut gon bieu thuc:\(\sqrt{\frac{a+\sqrt{a^2-b}}{2}}+\frac{a\sqrt{a^2-b}}{2}\)
Rut gon bieu thuc: \(\frac{a-b}{\sqrt{a}-\sqrt{b}}+\frac{\sqrt{a}^3+\sqrt{b}^3}{a-b}\)
\(\frac{a-b}{\sqrt{a}-\sqrt{b}}+\frac{\sqrt{a}^3+\sqrt{b}^3}{a-b}\)
\(=\sqrt{a}+\sqrt{b}+\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\sqrt{a}+\sqrt{b}+\frac{a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}\)
\(=\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}+\frac{a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}\)
\(=\frac{a-b+a-\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}\)
\(=\frac{2a-\sqrt{ab}}{\sqrt{a}-\sqrt{b}}\)
Rut gon
A=\(\left(\frac{2\sqrt{a}}{\sqrt{a}+3}+\frac{\sqrt{a}}{\sqrt{a}-3}-\frac{3a+3}{a-9}\right):\left(\frac{2\sqrt{a}-2}{\sqrt{a}-3}-1\right)\)
a) rut gon A
b)Tìm a để >hoặc bang \(\frac{-1}{3}\)
c)tìm giá trị nho nhất của A
Rut gon bieu thuc sau
\(\sqrt{\frac{a}{b}}+\sqrt{ab}+\frac{a}{b}\sqrt{\frac{b}{a}}\) voi a > 0 va b > 0
\(\sqrt{\frac{a}{b}}+\sqrt{ab}+\frac{a}{b}\sqrt{\frac{b}{a}}\)
\(=\sqrt{\frac{a}{b}}+\sqrt{ab}+\sqrt{\frac{a^2b}{b^2a}}\)
\(=\sqrt{\frac{a}{b}}+\sqrt{ab}+\sqrt{\frac{a}{b}}\)
\(=2\sqrt{\frac{a}{b}}+\sqrt{ab}\)
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\(A=\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)
Rut gon A
tham khao nha
\(A=\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)
\(A=\left(\frac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{a}\left(\sqrt{b}-\sqrt{a}\right)}\right):\left(\frac{\sqrt{b}+\sqrt{a}}{\sqrt{ab}}\right)\)
\(A=\left(\frac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}-\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}\right).\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)
\(A=\frac{a-2\sqrt{ab}+b}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}.\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)
\(A=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}.\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)
\(A=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
vay \(A=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
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ĐK : tự ghi nha
\(\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)
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Cho bieu thuc:
P=\(\frac{1}{\sqrt{x}+2}-\frac{5}{x-\sqrt{x}-6}-\frac{\sqrt{x}-2}{3-\sqrt{x}}\)
a. Rut gon bieu thuc P
b.Tim GTLN cua P sau khi rut gon
đk: x>=0; x khác 3
a) \(P=\frac{\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}-\frac{5}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}+\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}-3}=\frac{\sqrt{x}-3-5+x-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\frac{x+\sqrt{x}-12}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\)
\(P=\frac{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\frac{\sqrt{x}+4}{\sqrt{x}+2}\)
b) \(P=\frac{\sqrt{x}+2+2}{\sqrt{x}+2}=1+\frac{2}{\sqrt{x}+2}\)
ta có: \(x\ge0\Rightarrow\sqrt{x}\ge0\Leftrightarrow\sqrt{x}+2\ge2\Leftrightarrow\frac{2}{\sqrt{x}+2}\le1\Leftrightarrow1+\frac{2}{\sqrt{x}+2}\le2\Rightarrow MaxP=2\Rightarrow x=0\)
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