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a)\(=\frac{1}{7}\)
b)\(=\frac{1}{3}\)
quy đồng \(\frac{1}{7}=\frac{3.1}{3.7}=\frac{3}{21}\)
\(\frac{1}{3}=\frac{7.1}{7.3}=\frac{7}{21}\)
\(\frac{3}{21}+\frac{7}{21}=\frac{9}{21}=\frac{3}{7}\)
Ta co:
\(\frac{5+a}{8a}\)= \(\frac{-1}{12}\)
<=> 12(5+a)=-8a
<=>60+12a=-8a
<=>-20a=60
<=>a=-3
nhớ mik nha:)
theo bài ra ta có \(\frac{a+5}{8a}\)=\(\frac{-1}{12}\)suy ra (5+a).12=-8a suy ra 60+12a+8a=0 suy ra 20a=-60 suy ra a=-3
vậy..............
C = \(\frac{1010}{\left(1010-2\right).8-994}\)
= \(\frac{1010}{1010.8-2.8-994}\)
=\(\frac{1010}{1010.\left(8-1\right)}\)
=\(\frac{1}{7}\)
D = \(\frac{1.2.3.\left(1+2^3+3^3+5^3\right)}{1.3.6.\left(1+2^3+3^3+5^3\right)}\)
= \(\frac{1}{3}\)
Quy đồng ta được 2 phân số là: \(\frac{3}{21};\frac{7}{21}\)
\(\frac{1.2.3+2.4,6+4.8.12+7.14.21}{1.3.5+2.6.10+4.12.20+7.21.35}\)
\(=\frac{1\left(1.2.3\right)+2\left(1.2.3\right)+4\left(1.2.3\right)+7\left(1.2.3\right)}{1\left(1.3.5\right)+2\left(1.3.5\right)+4\left(1.2.3\right)+7\left(1.2.3\right)}\)
\(=\frac{6\left(1+2+4+7\right)}{15\left(1+2+4+7\right)}=\frac{6}{15}=\frac{3}{5}\)
\(C=\dfrac{1010}{7710}=\dfrac{101}{771}=\dfrac{48783}{771\cdot483}\)
\(D=\dfrac{6+2\cdot4\cdot6+3\cdot6\cdot9+125\cdot6}{6\cdot3+6\cdot24+6\cdot81+6\cdot375}\)
\(=\dfrac{1+2\cdot4+3\cdot6+125}{3+24+81+375}=\dfrac{152}{483}=\dfrac{117192}{483\cdot771}\)
mà 48783<117192
nên C<D
\(A=\frac{2.6.10+4.12.20+6.18.30+...+20.60.100}{1.2.3+2.4.6+3.6.9+...+10.20.30}\)
=> \(A=\frac{2^3.1.3.5+4^3.1.3.5+6^3.1.3.5+...+20^3.1.3.5}{1.2.3+2^3.1.2.3+3^3.1.2.3+...+10^3.1.2.3}\)
=> \(A=\frac{1.3.5\left(2^3+4^3+6^3+...+20^3\right)}{1.2.3\left(1+2^3+3^3+...+10^3\right)}=\frac{1.5.2^3.\left(1+2^3+3^3+...+10^3\right)}{1.2.\left(1+2^3+3^3+...+10^3\right)}\)
=> \(A=5.2^2=20\)
Đáp số: A=20
\(\frac{2\cdot6\cdot10+4\cdot12\cdot20+...+20\cdot60\cdot100}{1\cdot2\cdot3+2\cdot4\cdot6+...+10\cdot20\cdot30}=\frac{10\cdot2\left(1\cdot2\cdot3+2\cdot4\cdot6+...+10\cdot20\cdot30\right)}{1\cdot2\cdot3+2\cdot4\cdot6+...+10\cdot20\cdot30}\)
\(=20\)