A = \(\frac{\frac{3}{4}-\frac{3}{11}+\frac{3}{13}}{\frac{5}{4}-\frac{5}{11}+\frac{5}{13}}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{4}-\frac{5}{6}+\frac{5}{8}}\)

\(=\frac{3.\left(\frac{1}{4}-\frac{1}{11}+\frac{1}{13}\right)}{5.\left(\frac{1}{4}-\frac{1}{11}+\frac{1}{13}\right)}+\frac{\frac{1}{2}-\frac{1}{3}+\frac{1}{4}}{\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}\right)}\)

\(=\frac{3}{5}+\frac{1}{\frac{5}{2}}\)

\(=\frac{3}{5}+\frac{2}{5}=1\)

b) B = \(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6.8^4.3^5}-\frac{5^{10}.7^3:25^5.49}{\left(125.7\right)^3+5^9.14^3}\)

\(=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.7^2}{\left(5^3\right)^3.7^3+5^9.\left(7.2\right)^3}\)

\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}-7^2}{5^9.7^3+5^9.7^3.2^3}\)

\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^2.\left(7-1\right)}{5^9.7^3\left(1+2^3\right)}\)

 \(=\frac{1}{3.2}-\frac{5.2}{7.3}\)

\(=\frac{7}{3.2.7}-\frac{5.2.2}{7.3.2}\)

\(=\frac{7}{42}-\frac{20}{42}\)

\(=-\frac{13}{42}\)

Mình làm câu này  các câu khác tương tự 

Mấu chốt làm bài này là đưa về thừa số nguyên tố

\(\frac{12^7.3^{35}.14^{21}}{9^{21}.7^{21}.2^{35}}=\frac{3^7.4^7.3^{35}.2^{21}.7^{21}}{3^{2.21}.7^{21}.2^{35}}=\frac{3^7.2^{2.7}.3^{35}.2^{21}.7^{21}}{3^{2.21}.7^{21}.2^{35}}=\frac{3^7.2^{14}.3^{35}.2^{21}.7^{21}}{3^{42}.7^{21}.2^{35}}=\frac{3^{42}.2^{35}.7^{21}}{3^{42}.7^{21}.2^{35}}=1\)

Có 2 cách 

C1:  \(\frac{x}{21}=\frac{y}{14}\Rightarrow\frac{3x}{63}=\frac{7y}{98}=\frac{3x-7y}{63-98}=\frac{70}{-35}=-2\\ \)=> \(\hept{\begin{cases}3x=63.\left(-2\right)\\7y=98\left(-2\right)\end{cases}\Rightarrow\hept{\begin{cases}x=-42\\y=-28\end{cases}}}\)

C2

\(\frac{x}{21}=\frac{y}{14}\Rightarrow x=\frac{21}{14}y=\frac{3}{2}y\\ \)

Mà \(3x-7y=70\Rightarrow3.\frac{3}{2}y-7y=70\Rightarrow-\frac{5}{2}y=70\Rightarrow y=-28\Rightarrow x=-42\)

\(\frac{9^2}{3^4-3^3}=\frac{3^4}{3^4-3^3}=\frac{3^4}{3^3\left(3-1\right)}=\frac{3}{2}\\ \)

không hiểu cái đề bài của bạn luôn 

\(-8^3\times2^{3n}=4^{2n}\times164\)

Mình giúp bạn edit lại đề dù mình ko giải cho bạn đc. Sorry.

a) Ta có : A = |x - 3| + |x - 5| 

                   = |3 - x| + |x - 5|

                 \(\ge\)|3 - x + x - 5|

                   = | - 2|

                   = 2

Dấu "=" xảy ra <=> (x - 3)(x - 5) = 0

                           => \(\orbr{\begin{cases}x-3=0\\x-5=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=5\end{cases}}}\)

Vậy MinA = 2 khi x = 3 hoặc x = 5

b) Ta có B = |x + 1| + |7 - x| 

              \(\ge\)|x + 1 + 7 - x|

                =  |8|

                = 8

Dấu "=" xảy ra <=> (x + 1)(x - 7) = 0

                          => \(\orbr{\begin{cases}x+1=0\\x-7=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=7\end{cases}}\)

Vậy MinB = 8 khi x = - 1 hoặc x = 7

THANK YOU XYZ !!!

a) \(|2x-2,5|=|x-1,7|\)

\(\Leftrightarrow\orbr{\begin{cases}2x-2,5=x-1,7\\2x-2,5=1,7-x\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x-x=-1,7+2,5\\2x+x=1,7+2,5\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{4}{5}\\x=\frac{7}{5}\end{cases}}\)

Vậy ...

b) \(|x+1|-|\frac{1}{2}x-3|=0\)

\(\Leftrightarrow|x+1|=|\frac{1}{2}x-3|\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=\frac{1}{2}x-3\\x+1=3-\frac{1}{2}x\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{2}x=-3-1\\x+\frac{1}{2}x=3-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=-8\\x=\frac{4}{3}\end{cases}}\)

Vậy ...

cảm ơn bạn nhé