\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2.\left(3+2.6+7.21\right)}{5.\left(3+2.6+7.21\right)}=\frac{2}{5}\)

\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2.3+8.3+98.3}{3.5+3.20+3.45}=\frac{3.\left(2+8+98\right)}{3.\left(5+20+45\right)}=\frac{108}{70}=\frac{54}{35}=1\frac{19}{35}\)

rút gọn PS

3.7.13.37.39-10101/505050-70707

làm bài dưới :

rút gọn phân số : 

\(\frac{3.7.13.37.39-10101}{505050-70707}\)

\(=\frac{10101.39-10101}{50.10101-7.10101}\)

\(=\frac{10101.\left(39-1\right)}{10101.\left(50-7\right)}\)

\(=\frac{38}{43}\)

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)

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

\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2.3+4.6+2.7.3.7}{3.5+2.3.5.2+3.7.5.7}\)

\(=\frac{6.1+4.6+6.49}{15.1+15.4+15.49}\)

\(=\frac{6\left(1+4+49\right)}{35\left(1+4+49\right)}=\frac{6}{35}\)

tren tu : dat 2.3 ra ngoai

trong ngoặc: 1+2.2+7.7

dưới mẫu : dat 3.5 ra ngoai

trong ngoặc: 1+2.2+7.7

rút gọn: 2.3/3.5=2/5

cho mk vs

\(\dfrac{2\cdot3+4\cdot6+14\cdot21}{3\cdot5+6\cdot10+21\cdot35}=\dfrac{2\left(3+2\cdot3+7\cdot21\right)}{3\left(5+2\cdot10+7\cdot35\right)}=\dfrac{2\cdot3\left(1+2\cdot3+7\cdot5\right)}{3\cdot5\left(1+2\cdot3+7\cdot5\right)}=\dfrac{2}{5}\)

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

\(=\dfrac{6+24+294}{15+60+735}\)

\(=\dfrac{324}{810}\)

\(=\dfrac{2}{5}\)

\(\dfrac{2.3+4.6+14.21}{3.5+6.10+21.35}=\dfrac{2.3+\left(2.3\right).2^2+\left(2.3\right).7^2}{3.5+\left(3.5\right).2^2+\left(3.5\right).7^2}\\ \\ \\ \\ =\dfrac{2.3.\left(1+2^2+7^2\right)}{3.5.\left(1+2^2+7^2\right)}\\ \\ \\ \\ =\dfrac{2.3}{3.5}=\dfrac{2}{5}\)

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

=\(\frac{2\left(3+2.6+7.21\right)}{5\left(3+2.6+7.21\right)}\)

=\(\frac{2}{5}\)

ta có:

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

bài trên có các số ở tử và mẫu giống nhau đó là: 21;6;3

=>ta cho chúng hết cho nhau

vậy ta còn phân số:

\(\frac{2+4+14}{3+10+35}\)

=\(\frac{20}{48}\)=\(\frac{5}{12}\)

\(\frac{2.3+4.6+14.21}{3.5+6.10+21.35}=\frac{2+4+14}{5+10+35}=\frac{20}{40}=\frac{1}{2}\)Tự tính

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

= \(\dfrac{2.3+8.3+98.3}{3.5+3.20+245.3}\)

= \(\dfrac{3.\left(2+8+98\right)}{3.\left(5+20+245\right)}\)

= \(\dfrac{3.108}{3.270}\)

= \(\dfrac{108}{270}\) = \(\dfrac{2}{5}\)

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!