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\(\frac{123.98-49.46}{63.48+126.76}\)
\(=\frac{3.41.2.7.7-7.7.2.23}{63.2.24+126.76}\)
\(=\frac{98.\left(123-23\right)}{126.\left(24+76\right)}\)
\(=\frac{98.100}{126.100}\)
\(=\frac{7}{9}\)
\(\text{Ta có :}\)\(-\frac{4.5+4.11}{8.7-4.3}=\frac{-4\left(5+11\right)}{4\left(2.7-3\right)}=\frac{-16}{24}=\frac{-4}{6}\)
\(\frac{-15.8+10.7}{5.6+20.3}=\frac{-5\left(3.8-2.7\right)}{5.\left(6+2.3\right)}=\frac{-10}{12}=\frac{-5}{6}\)
\(\text{Vì:}\)\(-\frac{4}{6}>\frac{-5}{6}\left(-4>-5\right)\)
\(\text{Nên :}\)\(-\frac{4.5+4.11}{8.7-4.3}>\)\(\frac{-15.8+10.7}{5.6+20.3}\)
\(-\frac{4.5+4.11}{8.7-4.3}=-\frac{4.\left(5+11\right)}{4.\left(14-3\right)}=-\frac{4.16}{4.11}=\frac{-16}{11}\)
\(\frac{-15.8+10.7}{5.6+20.3}=\frac{\left(-5\right).3.8+5.2.7}{5.2.3+2.2.5.3}=\frac{5.\left(-3.8+2.7\right)}{5.2.3.\left(1+2\right)}\)
\(=\frac{5.\left(-10\right)}{5.2.3.3}=\frac{-5}{9}\)
\(\frac{-5}{9}>\frac{-16}{11}\)
\(\frac{2019.2020-4040}{2017.2018+4034}\)=\(\frac{\left(2017+2\right).2020-4040}{2017.2018+2017.2}\)
=\(\frac{2017.2020+2.2020-4040}{2017.\left(2018+2\right)}\)
=\(\frac{2017.2020+4040-4040}{2017.2020}\)
=\(\frac{2017.2020+0}{2017.2020}\)
=\(\frac{1}{1}\)=1
\(\left(a-b\right)\left(a^2+ab+b^2\right)=a^3+a^2b+ab^2-ba^2-ab^2+b^3=a^3+b^3\)
\(3^{28}.4^{14}.18^{35}.19^7\)
\(=3^{28}.\left(2^2\right)^{14}.\left(2.3^2\right)^{35}.19^7\)
\(=3^{28}.2^{28}.2^{35}.3^{70}.19^7\)
\(=2^{63}.3^{98}.19^7\)
P/S: mấy bài này cứ phân tích ra các thừa số nguyên tố mà làm
\(A=\frac{a^3+2a^2-1}{a^3+2a^2+2a+1}\)
\(\Rightarrow A=\frac{\left(a^3+a^2\right)+\left(a^2-1\right)}{\left(a^3+a^2\right)+\left(a^2+a\right)+\left(a+1\right)}\) \(=\frac{a^2\left(a+1\right)+\left(a+1\right)+\left(a+1\right)}{a^2\left(a+1\right)+a\left(a+1\right)+\left(a+1\right)}\)
\(=\frac{\left(a+1\right)\left(a^2+a-1\right)}{\left(a+1\right)\left(a^2+a+1\right)}\)
\(=\frac{a^2+a-1}{a^2+a+1}\)
\(\frac{123\cdot98-49\cdot46}{63\cdot48+126\cdot76}\)
\(=\frac{12054-49\cdot46}{63\cdot48+126\cdot76}\)
\(=\frac{2\cdot3\cdot7^2\cdot41-49\cdot46}{63\cdot48+2^3\cdot3^2\cdot7\cdot19}\)
\(=\frac{7^2\left(2\cdot3\cdot41\right)-49\cdot46}{63\cdot48+3^2\cdot7\cdot\left(2^3\cdot19\right)}\)
\(=\frac{49\cdot246-49\cdot46}{63\cdot48+63\cdot152}\)
\(=\frac{49\left(246-46\right)}{63\left(48+152\right)}\)
\(=\frac{49\cdot200}{63\cdot200}\)
\(=\frac{49}{63}=\frac{7}{9}\)
=7/9
k mk nhé!!!