\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)

\(=\frac{14}{6}+\frac{1}{3}+\frac{14}{9}+\frac{7}{15}+\frac{14}{14}+\frac{6}{4}\)

\(=\frac{42+6+28}{18}+\frac{7}{15}+\frac{2}{2}+\frac{3}{2}\)

\(=\frac{76}{18}+\frac{7}{15}+\frac{5}{2}\)

\(=\frac{76}{18}+\frac{5}{2}+\frac{7}{15}\)

\(=\frac{76+45}{18}+\frac{7}{15}\)

\(=\frac{121}{18}+\frac{7}{15}\)

\(=\frac{605+42}{90}\)

\(=\frac{647}{90}\)

\(\frac{14}{6}+\frac{1}{3}+\frac{14}{14}+\frac{14}{9}+\frac{7}{15}+\frac{6}{4}\)

\(=(\frac{7}{3}+\frac{1}{3})+1+(\frac{14}{9}+\frac{7}{15})+\frac{3}{2}\)

\(=\frac{8}{3}+1+\frac{91}{45}+\frac{3}{2}\)

\(=2+\frac{2}{3}+1+2+\frac{1}{45}+1+\frac{1}{2}\)

\(=\left(\frac{2}{3}+\frac{1}{45}+\frac{1}{2}\right)+\left(2+1+2+1\right)\)

\(=1+\frac{17}{90}+6\)

\(=7+\frac{17}{90}\)

\(=7\frac{17}{90}\)

a) $\frac{4}{{25}}:\frac{4}{3} = \frac{4}{{25}} \times \frac{3}{4} = \frac{3}{{25}}$ 

b) $\frac{3}{{14}}:\frac{6}{7} = \frac{3}{{14}} \times \frac{7}{6} = \frac{{3 \times 7}}{{14 \times 6}} = \frac{{3 \times 7}}{{7 \times 2 \times 3 \times 2}} = \frac{1}{4}$

c) $\frac{{12}}{{15}}:2 = \frac{{12}}{{15}} \times \frac{1}{2} = \frac{{12 \times 1}}{{15 \times 2}} = \frac{{6 \times 2 \times 1}}{{15 \times 2}} = \frac{6}{{15}}$           

d) $\frac{{21}}{8}:6 = \frac{{21}}{8} \times \frac{1}{6} = \frac{{21 \times 1}}{{8 \times 6}} = \frac{{7 \times 3 \times 1}}{{8 \times 3 \times 2}} = \frac{7}{{16}}$

= -5/8 + 14/25 - 3/8

=( -5/8 - 3/8)+ 14/25

= -1 + 14/25

= -11/25

5/-8 + 14/25 - 6/16

= 5/-8 + 14/25 - 3/8

= -5/8 + 14/25 - 3/8

= ( -5/8 - 3/8 ) + 14/25

= -1 + 14/25

= -11/25 

chúc bn hok tốt

\(\frac{2}{\left(x+2\right)\left(x+4\right)}+\frac{4}{\left(x+4\right)\left(x+8\right)}+\frac{6}{\left(x+8\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Rightarrow\frac{1}{x+2}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+8}+\frac{1}{x+8}-\frac{1}{x+14}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Rightarrow\frac{1}{x+2}-\frac{1}{x+14}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Rightarrow\frac{x+14}{\left(x+2\right)\left(x+14\right)}-\frac{x+2}{\left(x+2\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Rightarrow\frac{x+14-x+2}{\left(x+2\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Rightarrow\frac{12}{\left(x+2\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

=> x = 12

\(\frac{14-6\sqrt{5}+8}{\sqrt{14-6\sqrt{5}}+1}=\frac{22-6\sqrt{5}}{\sqrt{\left(3-\sqrt{5}\right)^2}+1}=\frac{22-6\sqrt{5}}{4-\sqrt{5}}=\frac{\left(22-6\sqrt{5}\right)\left(4+\sqrt{5}\right)}{16-5}=\frac{58-2\sqrt{5}}{11}\)

\(\frac{2}{\left(x+2\right)\left(x+4\right)}+\frac{4}{\left(x+4\right)\left(x+8\right)}+\frac{6}{\left(x+8\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(=\frac{1}{x+2}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+8}+\frac{1}{x+8}-\frac{1}{x+14}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(=\frac{1}{x+2}-\frac{1}{x+14}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(=\frac{x+16}{\left(x+2\right)\left(x+14\right)}-\frac{x+2}{\left(x+2\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(=\frac{8}{\left(x+2\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Rightarrow x=8\)

\(a,\frac{20^{12}\cdot6^{14}}{8^{13}\cdot15^{12}}\)

\(=\frac{5^{12}\cdot2^{24}\cdot2^{14}\cdot3^{14}}{2^{39}\cdot3^{12}\cdot5^{12}}\)

\(=\frac{5^{12}\cdot2^{38}\cdot3^{14}}{2^{39}\cdot3^{12}\cdot5^{12}}=\frac{3^2}{2}=\frac{9}{2}\)

\(b,\frac{45^{12}\cdot10^{14}}{18^{13}\cdot25^{12}}\)

\(=\frac{5^{12}\cdot3^{24}\cdot2^{14}\cdot5^{14}}{2^{13}\cdot3^{26}\cdot5^{24}}\)

\(=\frac{5^{26}\cdot3^{24}\cdot2^{14}}{2^{13}\cdot3^{26}\cdot5^{24}}=\frac{5^2\cdot2}{3^2}=\frac{50}{9}\)

\(c,\frac{18^{12}\cdot27^8}{6^8\cdot3^{40}}\)

\(=\frac{2^{12}\cdot3^{24}\cdot3^{24}}{2^8\cdot3^8\cdot3^{40}}\)

\(=\frac{2^{12}\cdot3^{48}}{2^8\cdot3^{48}}=2^4=16\)

\(d,\frac{12^{14}\cdot9^{18}}{8^9\cdot27^{17}}\)

\(=\frac{3^{14}\cdot2^{28}\cdot3^{36}}{2^{27}\cdot3^{51}}\)

\(=\frac{3^{50}\cdot2^{28}}{2^{27}\cdot3^{51}}=\frac{2}{3}\)

làm hơi tắt nên chịu khó hiểu

     \(\frac{2}{\left(x+2\right)\left(x+4\right)}+\frac{4}{\left(x+4\right)\left(x+8\right)}+\frac{6}{\left(x+8\right)\left(x+14\right)}=\frac{x}{\left(x+2\right)\left(x+14\right)}\)

\(\Leftrightarrow\frac{x}{\left(x+2\right)\left(x+14\right)}=\frac{1}{x+2}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1}{x+8}-\frac{1}{x+8}-\frac{1}{x+14}\)

\(\Leftrightarrow\frac{x}{\left(x+2\right)\left(x+14\right)}=\frac{1}{x+2}-\frac{1}{x+14}\)

\(\Leftrightarrow\frac{x}{\left(x+2\right)\left(x+14\right)}=\frac{\left(x+14\right)-\left(x+2\right)}{\left(x+2\right)\left(x+14\right)}\)

\(\Leftrightarrow x=\left(x+14\right)-\left(x+2\right)\)

\(\Leftrightarrow x=x+14-x-2\)

\(\Leftrightarrow x=\left(x-x\right)+\left(14-2\right)\)

\(\Leftrightarrow x=0+12\)

\(\Leftrightarrow x=12\)

x=12

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