\(\frac{2.3+6.9+10.15+14.21}{2.5+6.15+10.25+14.35}\)

Rút gọn:

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

\(=\frac{12}{5}\)

\(\frac{2.3+6.9+10.15+14.21}{2.5+6.15+10.25+14.35}=\frac{2.3+6.3.3+10.5.3+14.7.3}{2.5+6.3.5+10.5.5+14.7.5}\)

\(=\frac{3\left(2.1+6.3+10.5+14.7\right)}{5\left(2.1+6.3+10.5+14.7\right)}=\frac{3}{5}\)

\(\frac{1.2+1.4+3.6+4.8}{2.3+4.6+6.9+8.12}\)

=\(\frac{1.2}{2.3}\)+\(\frac{1.4}{4.6}\)+\(\frac{3.6}{6.9}\)+\(\frac{4.8}{8.12}\)

= \(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{3}\)+\(\frac{1}{3}\)

= \(\frac{2}{6}+\frac{1}{6}+\frac{2}{6}+\frac{2}{6}\)

=\(\frac{7}{6}\)

Mình nghĩ đề bài phải là:

          \(\frac{1.2+2.4+3.6+4.8}{2.3+4.6+6.9+8.12}\)   *2.3 + 4.6 + 6.9 + 8.12 = 3.(1.2 + 2.4 + 3.6 + 4.8)*

\(=\)\(\frac{1\left(1.2+2.4+3.6+4.8\right)}{3\left(1.2+2.4+3.6+4.8\right)}\)

\(=\)\(\frac{1}{3}\)

14/45

b) \(\dfrac{6\cdot9-2\cdot17}{63\cdot3-119}\)

\(=\dfrac{2\left(3\cdot9-17\right)}{7\cdot\left(3\cdot9-17\right)}\)

\(=\dfrac{2}{7}\)

2.3+4.6+14.21/3.5+6.10+21.35

= 2 . 3 + 2 . 2 . 3 . 2 + 7 .

\(\frac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}\)=\(\frac{2\cdot3\cdot\left(1+2\cdot2+7\cdot7\right)}{3\cdot5\cdot\left(1+2\cdot2+7\cdot7\right)}\)

Sau đó ta chia tử và mẫu cho (1+2*2+7*7) thì ta có phân số

\(\frac{2\cdot3}{3\cdot5}\)=\(\frac{2}{5}\)(rút gọn tử và mẫu cho 3)

..............

\(\dfrac{2^3.3^4}{2^3.3^2.5}=\dfrac{1.3^2}{1.1.5}=\dfrac{9}{5}\)

Ta có :2^3.3^4/2^2.3^2.5=2.3^2/1.1.5=2.9/5=\(\dfrac{18}{5}\)

Giải:

a) \(\dfrac{5^3.90.4^3}{25^2.3^2.2^{13}}\) 

\(=\dfrac{5^3.5.3^2.2.\left(2^2\right)^3}{\left(5^2\right)^2.3^2.2^{13}}\) 

\(=\dfrac{5^4.3^2.2.2^6}{5^4.3^2.2^{13}}\) 

\(=\dfrac{5^4.3^2.2^7}{5^4.3^2.2^{13}}\) 

\(=\dfrac{1}{2^6}=\dfrac{1}{64}\) 

b) \(\dfrac{15^2.16^4-15^3.16^3}{12^2.20^3-20^2.12^3}\) 

\(=\dfrac{15^2.16^3.16-15^2.16^3.15}{12^2.20^2.20-20^2.12^2.12}\) 

\(=\dfrac{15^2.16^3.\left(16-15\right)}{12^2.20^2.\left(20-12\right)}\) 

\(=\dfrac{\left(3.5\right)^2.\left(2^4\right)^3.1}{\left(3.2^2\right)^2.\left(2^2.5\right)^2.8}\) 

\(=\dfrac{3^2.5^2.2^{12}}{3^2.\left(2^2\right)^2.\left(2^2\right)^2.5^2.2^3}\) 

\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^4.2^4.2^3}\) 

\(=\dfrac{3^2.5^2.2^{12}}{3^2.5^2.2^{11}}\) 

\(=2\) 

c) \(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}\) 

\(=\dfrac{2.3+2.3.2.2+2.3.7.7}{3.5+3.5.2.2+3.5.7.7}\) 

\(=\dfrac{2.3+2.3.4+2.3.49}{3.5+3.5.4+3.5.49}\) 

\(=\dfrac{2.3.\left(1+4+49\right)}{3.5.\left(1+4+49\right)}\) 

\(=\dfrac{2.3}{3.5}\) 

\(=\dfrac{2}{5}\) 

Chúc bạn học tốt!