Rút gọn:`78/45=[78:3]/[45:3]=26/15`

Tính:`13/17+31/34=26/34+31/34=57/34`

Rút gọn phân số: \(\dfrac{78}{45}=\dfrac{78:3}{45:3}=\dfrac{26}{15}\)

Tính: \(\dfrac{13}{17}+\dfrac{31}{34}=\dfrac{26}{34}+\dfrac{31}{34}=\dfrac{57}{34}\)

\(=\)\(\dfrac{78:3}{45:3}=\dfrac{26}{15}\)

\(=\dfrac{26}{34}+\dfrac{31}{34}=\dfrac{57}{34}\)

Lời giải:
$\frac{20}{12}+\frac{36}{18}-\frac{21}{28}=\frac{5}{3}+2-\frac{3}{4}$

$=\frac{20}{12}+\frac{24}{12}-\frac{9}{12}=\frac{20+24-9}{12}=\frac{35}{12}$

\(=\dfrac{5}{3}+2-\dfrac{3}{4}=\dfrac{5.4+2.12-3.3}{12}=\dfrac{20+24-9}{12}=\dfrac{35}{12}\)

\(\dfrac{70}{80}-\dfrac{2}{16}-\dfrac{3}{24}\)
\(=\dfrac{7}{8}-\dfrac{1}{8}-\dfrac{1}{8}=\dfrac{5}{8}\)

`70/80-2/16-3/24`

`=7/8-1/8-1/8`

`=5/8`

3/8+5/8=1

=\(\dfrac{3}{8}\)+\(\dfrac{3}{4}\)=\(\dfrac{3}{8}\)+\(\dfrac{6}{8}\)=\(\dfrac{9}{8}\)

=3/8+5/8=1

\(\dfrac{4}{5}\times\dfrac{4}{3}=\dfrac{16}{15}\)

4/5×4/3=1615

\(=\dfrac{4}{5}\cdot\dfrac{4}{3}=\dfrac{16}{15}\)

\(\dfrac{60}{72}=\dfrac{60:12}{72:12}=\dfrac{5}{6}\\ \dfrac{70}{95}=\dfrac{70:5}{95:5}=\dfrac{14}{19}\\ \dfrac{150}{360}=\dfrac{150:30}{360:30}=\dfrac{5}{12}\)

\(\dfrac{60}{72}=\dfrac{5}{6}\)

\(\dfrac{70}{95}=\dfrac{14}{19}\)

\(\dfrac{150}{360}=\dfrac{5}{12}\)

\(\dfrac{3}{12}+\dfrac{1}{4}=\dfrac{3:3}{12:3}+\dfrac{1}{4}=\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{2}{4}=\dfrac{1}{2}\)

\(\dfrac{4}{10}+\dfrac{3}{5}=\dfrac{4:2}{10:2}+\dfrac{3}{5}=\dfrac{2}{5}+\dfrac{3}{5}=\dfrac{5}{5}=1\)

\(\dfrac{12}{27}+\dfrac{2}{9}=\dfrac{12:3}{27:3}+\dfrac{2}{9}=\dfrac{4}{9}+\dfrac{2}{9}=\dfrac{6}{9}=\dfrac{2}{3}\)

\(\dfrac{7}{3}+\dfrac{20}{15}=\dfrac{7}{3}+\dfrac{20:5}{15:5}=\dfrac{7}{3}+\dfrac{4}{3}=\dfrac{11}{3}\)

a, 15/25 - 3/21 = 3/5 - 1/7 = 21/35 - 5/35 = 18/35

b, 24/36 - 6/12 = 2/3 - 1/2 = 4/6 - 3/6 = 1/6

a)15/25-3/21=3/5-1/7=16/35                b)24/36-6/12=2/3-1/2=1/6

Cảm ơn

Đặt `A=(1-3x)/(2x)+(3x-2)/(2x-1)+(3x-2)/(2x-4x^2)`

`=(2x(3x-2))/(2x(2x-1))-((3x-1)(2x-1))/(2x(2x-1))-(3x-2)/(2x(2x-1))`

`=(6x^2-4x-6x^2+5x-1-3x+2)/(2x(2x-1))`

`=(-2x+1)/(2x(2x-1))`

`=-1/(2x)`

`2x=1/(483)`

`=>A=-1/(1/483)=-483`

\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x-4x^2}\)

⇔\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}+\dfrac{3x-2}{2x\left(1-2x\right)}\)

⇔\(\dfrac{1-3x}{2x}+\dfrac{3x-2}{2x-1}-\dfrac{(3x-2)}{2x\left(2x-1\right)}\)

ĐKXĐ: \(\left\{{}\begin{matrix}2x\ne0\\2x-1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\2x\ne1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne\dfrac{1}{2}\end{matrix}\right.\)

MTC: 2x(2x-1)

\(\dfrac{1-3x\left(2x-1\right)}{2x\left(2x-1\right)}+\dfrac{(3x-2)(2x)}{(2x-1)(2x)}-\dfrac{(3x-2)}{2x\left(2x-1\right)}\)

\(\Rightarrow1-3x\left(2x-1\right)+\left(3x-2\right)\left(2x\right)-\left(3x-2\right)\)

\(\Leftrightarrow1-6x^2+3x+6x^2-4x-3x+2\\ \Rightarrow-4x+3\)

Thay \(x=\dfrac{1}{966}\)vào biểu thức trên

ta có -4x+3= \(-4\times\dfrac{1}{966}+3=\dfrac{-4}{966}+3=\dfrac{-2}{483}+3=\dfrac{-2}{483}+\dfrac{1449}{483}=\dfrac{1447}{483}\)