2)

\(2+\dfrac{5}{7}+\left(\dfrac{\dfrac{3}{19}+\dfrac{3}{23}-\dfrac{3}{28}}{\dfrac{5}{19}+\dfrac{5}{23}-\dfrac{5}{28}}\right)\cdot x=\dfrac{20}{7}\\ \left[\dfrac{3\cdot\left(\dfrac{1}{19}+\dfrac{1}{23}-\dfrac{1}{28}\right)}{5\cdot\left(\dfrac{1}{19}+\dfrac{1}{23}-\dfrac{1}{28}\right)}\right]\cdot x=\dfrac{20}{7}-\dfrac{5}{7}-2\\ \dfrac{3}{5}x=\dfrac{15}{7}-2\\ \dfrac{3}{5}x=\dfrac{1}{7}\\ x=\dfrac{5}{21}\)

đấy nhá

b) Ta có: \(\left|x\right|-\dfrac{3}{4}=\dfrac{5}{3}\)

\(\Leftrightarrow\left|x\right|=\dfrac{5}{3}+\dfrac{3}{4}=\dfrac{20}{12}+\dfrac{9}{12}=\dfrac{29}{12}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{29}{12}\\x=-\dfrac{29}{12}\end{matrix}\right.\)

c) Ta có: \(\left|2x-\dfrac{1}{3}\right|+\dfrac{5}{6}=1\)

\(\Leftrightarrow\left|2x-\dfrac{1}{3}\right|=\dfrac{1}{6}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{1}{3}=\dfrac{1}{6}\\2x-\dfrac{1}{3}=\dfrac{-1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{1}{6}+\dfrac{1}{3}=\dfrac{1}{2}\\2x=\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=\dfrac{1}{12}\end{matrix}\right.\)

\(a.C=\dfrac{x^4+x^8+x^{12}+x^{16}+x^{20}+x^{24}+x^{28}+1}{x^3+x^7+x^{11}+x^{15}+x^{19}+x^{23}+x^{27}+x^{31}}=\dfrac{x^{28}+x^{24}+...+x^8+x^4+1}{x^3\left(x^{28}+x^{24}+...+x^8+x^4+1\right)}=\dfrac{1}{x^3}\) Tại x = 2015 thì : \(C=\dfrac{1}{x^3}=\dfrac{1}{2015^3}\)

\(b.F=\dfrac{1}{1.2.3.4}+\dfrac{1}{2.3.4.5}+\dfrac{1}{3.4.5.6}+...+\dfrac{1}{2011.2012.2013.2014}\)

\(3F=\dfrac{3}{1.2.3.4}+\dfrac{3}{2.3.4.5}+\dfrac{3}{3.4.5.6}+...+\dfrac{3}{2011.2012.2013.2014}\)

\(3F=\dfrac{1}{1.2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{2.3.4}-\dfrac{1}{3.4.5}+\dfrac{1}{3.4.5}-\dfrac{1}{4.5.6}+...+\dfrac{1}{2011.2012.2013}-\dfrac{1}{2012.2013.2014}\)

\(3F=\dfrac{1}{1.2.3}-\dfrac{1}{2012.2013.2014}\)

Tới đây dễ rồi , bạn tự tính nốt .

yêu cầu đề?!

a: \(\Leftrightarrow\dfrac{x+5}{2x-1}+\dfrac{2x-1}{x+5}-2=0\)

\(\Leftrightarrow\left(x+5\right)\left(x+5\right)+\left(2x-1\right)^2-2\left(2x-1\right)\left(x+5\right)=0\)

\(\Leftrightarrow x^2+10x+25+4x^2-4x+1-2\left(2x^2+10x-x-5\right)=0\)

\(\Leftrightarrow5x^2+6x+26-4x^2-18x+10=0\)

\(\Leftrightarrow x^2-12x+36=0\)

=>x=6

b: \(\dfrac{9x-27}{2x-7}-\dfrac{8x-28}{x-3}=0\)

\(\Leftrightarrow9\left(x-3\right)^2-4\left(2x-7\right)^2=0\)

\(\Leftrightarrow\left(3x-9\right)^2-\left(4x-14\right)^2=0\)

\(\Leftrightarrow\left(3x-9-4x+14\right)\left(3x-9+4x-14\right)=0\)

\(\Leftrightarrow\left(5-x\right)\left(7x-23\right)=0\)

hay \(x\in\left\{5;\dfrac{23}{7}\right\}\)

b: \(\Leftrightarrow\left(\dfrac{29-x}{21}+1\right)+\left(\dfrac{27-x}{23}+1\right)+\left(\dfrac{25-x}{25}+1\right)+\left(\dfrac{23-x}{27}+1\right)+\left(\dfrac{21-x}{29}+1\right)=0\)

=>50-x=0

hay x=50

c: \(\Leftrightarrow\dfrac{x-2}{2001}+1=\dfrac{x-1}{2002}+\dfrac{x}{2003}\)

\(\Leftrightarrow\left(\dfrac{x-2}{2001}-1\right)=\left(\dfrac{x-1}{2002}-1\right)+\left(\dfrac{x}{2003}-1\right)\)

=>x-2003=0

hay x=2003

\(\dfrac{x+1}{29}+\dfrac{x+3}{28}=\dfrac{x+5}{27}+\dfrac{x+7}{26}\)

<=>\(\dfrac{x+1}{29}+2+\dfrac{x+3}{28}+2=\dfrac{x+5}{27}+2+\dfrac{x+7}{26}+2\)

<=>\(\dfrac{x+59}{29}+\dfrac{x+59}{28}=\dfrac{x+59}{27}+\dfrac{x+59}{26}\)

<=>\(\left(x+59\right)\left(\dfrac{1}{29}+\dfrac{1}{28}-\dfrac{1}{27}-\dfrac{1}{26}\right)=0\)

vì 1/29+1/28-1/27-1/26 khác 0 =>x+59=0<=>x=-59

vậy....

Tính 1 câu thoy nhé !

\(\dfrac{3}{7}.19\dfrac{1}{3}-\dfrac{3}{7}.33\dfrac{1}{3}\)

= \(\dfrac{3}{7}.\left(19\dfrac{1}{3}-33\dfrac{1}{3}\right)\)

=\(\dfrac{3}{7}.-14=-6\)

a)\(x=\left(\dfrac{3}{56}\cdot\dfrac{28}{9}\right):\dfrac{-3}{7}=\dfrac{1}{6}:\dfrac{-3}{7}=-\dfrac{7}{18}\)

b)\(x=\left(\dfrac{7}{15}\cdot\dfrac{5}{3}\right)+\dfrac{3}{16}=\dfrac{7}{9}+\dfrac{3}{16}=\dfrac{139}{144}\)

c)\(x=\left(\dfrac{5}{6}-\dfrac{2}{5}\right).5=\dfrac{13}{6}\)

d)\(=>x\left(\dfrac{3}{4}-\dfrac{2}{5}\right)=\dfrac{1}{6}\cdot\left(\dfrac{3}{7}+\dfrac{5}{7}\right)\)

\(x\cdot\dfrac{7}{20}=\dfrac{4}{21}=>x=\dfrac{4}{21}\cdot\dfrac{20}{7}=\dfrac{80}{147}\)

d: \(\Leftrightarrow x^3+6x^2+12x+8-x^3+6x^2-12x+8=12x^2-12x-8\)

\(\Leftrightarrow12x^2+16=12x^2-12x-8\)

=>-12x=24

hay x=-2

e: \(\left(x+5\right)\left(x+2\right)-3\left(4x-3\right)=\left(x-5\right)^2\)

\(\Leftrightarrow x^2+7x+10-12x+9=x^2-10x+25\)

=>-5x+19=-10x+25

=>5x=6

hay x=6/5

f: \(\dfrac{x-5}{100}+\dfrac{x-4}{101}+\dfrac{x-3}{102}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)

=>x-105=0

hay x=105