\(\frac{a+5}{a-5}=\frac{b+6}{b-6}=>\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(=>a\left(b-6\right)+5\left(b-6\right)=a\left(b+6\right)-5\left(b+6\right)\)
\(=>ab-6a+5b-30=ab+6a-5b-30=>-6a+5b=6a-5b=>6a-\left(-6a\right)=5b-\left(-5b\right)\)
\(=>12a=10b=>\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\) (đpcm)
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)(\(a\ne5;b\ne6\))
Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
Cho A=\(1-\frac{1}{5}+\frac{1}{5^2}-...+\frac{1}{5^{2018}}\)
a, thu gọn a
b, cmr A<1/6
cho \(A=\frac{\left(85\frac{7}{30}-85\frac{5}{18}\right)-2\frac{2}{5}}{0,04}\).Tính 12,5% của A
cho \(B=\frac{\left(6\frac{3}{5}-3\frac{3}{14}\right)\cdot5\frac{5}{6}}{\left(21-1,25\right):2,5}\).Tính 5% của B
\(Cho:\frac{a}{5}=\frac{b}{6}=\frac{c}{7}\)
\(CMR:4\left(a-b\right)\left(b-c\right)=\left(c-a\right)^2\)
Thực hiện phép tính:
a) \(A=\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
b) \(B=81.\left[\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right].\frac{158158158}{711711711}\)
So sánh:
a, \(A=\frac{9^{99}+1}{9^{100}+1};B=\frac{10^{98}-1}{10^{99}-1}\)
b, \(A=\frac{5^{10}}{1+5+5^2+....+5^9};B=\frac{6^{10}}{1+6+6^2+....+6^9}\)
Giúp mk nhé! Ai làm nhanh nhất và hết mk tick cho.
So sánh:
\(A=\frac{5}{4x9}+\frac{5}{9x14}+\frac{5}{14x19}+...+\frac{5}{1704x1709}+\frac{5}{1709x1714}\)
\(B=\frac{6}{7x9}+\frac{6}{9x11}+\frac{6}{11x13}+...+\frac{6}{1283x1285}\)
( Làm xong nhớ kb với mk nhé )
a,\(A=a.\frac{1}{2}-a.\frac{2}{3}+a.\frac{3}{4}vớia=\frac{-6}{5}\)
b,\(B=\frac{-1}{6}.b+\frac{4}{3}.b-\frac{1}{2}.bvớib=\frac{-3}{7}\)
c,\(C=c.\frac{5}{4}+c.\frac{1}{6}-c.\frac{17}{12}vớic=\frac{2013}{2014}\)
cho \(M=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}....\frac{99}{100};N=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}....\frac{100}{101}\)
a/ so sánh M và N
b/ tính M nhân N
c/ CMR : M < 1 / 10
