Tìm giá trị lớn nhất của \(\frac{2020-x}{6-x}\)

Ta có : \(\frac{2020-x}{6-x}=\frac{6-x+2014}{6-x}=\frac{6-x}{6-x}+\frac{2014}{6-x}=1+\frac{2014}{6-x}\)

Đa thức lớn nhất \(\Leftrightarrow1+\frac{2014}{6-x}\)lớn nhất  \(\Rightarrow\frac{2014}{6-x}\)lớn nhất  \(\Rightarrow6-x\)nhỏ nhất và \(6-x>0\)

Mà \(x\in Z\)\(\Rightarrow x=5\)

Vậy giá trị lớn nhất của đa thức \(=\frac{2020-5}{6-5}=2020-5=2015\)\(\Leftrightarrow x=5\)

\(X-\left(\frac{31}{5}+\frac{31}{15}+\frac{31}{35}+\frac{31}{63}+\frac{31}{99}+\frac{31}{143}\right)=\frac{9}{13}\)

\(X-\left(\frac{31}{5}+\frac{31}{3\cdot5}+\frac{31}{5\cdot7}+\frac{31}{7\cdot9}+\frac{31}{9\cdot11}+\frac{31}{11\cdot13}\right)=\frac{9}{13}\)

\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)

\(X-\left[\frac{31}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)+\frac{31}{5}\right]=\frac{9}{13}\)

\(X-\left[\frac{31}{2}\cdot\frac{10}{39}+\frac{31}{5}\right]=\frac{9}{13}\)

\(X-\frac{1984}{195}=\frac{9}{13}\)

\(\Rightarrow X=\frac{9}{13}+\frac{1984}{195}=\frac{163}{15}\)

163 / 15

mk nghĩ v

\(A=\frac{544}{871}\)

Ý A CẬU CHỈ CẦN 

QUY ĐỒNG MẪU 18 VÀ 29 RỒI TÍNH

Ý B TƯƠNG TỰ

QUY ĐỒNG MẪU 

CỦA 12 VÀ 31

\(A=17\frac{2}{31}-\left(\frac{15}{17}+6\frac{2}{31}\right)=\left(17\frac{2}{31}-6\frac{2}{31}\right)-\frac{15}{17}=11-\frac{15}{17}=10+\left(1-\frac{15}{17}\right)=10\frac{2}{17}\)

\(B=\left(31\frac{6}{13}-36\frac{6}{13}\right)+5\frac{9}{41}=-5+5\frac{9}{41}=\frac{9}{41}\)

C=\(\left(27\frac{51}{59}-7\frac{51}{59}\right)+\frac{1}{3}=20+\frac{1}{3}=20\frac{1}{3}\)

\(D=\left(13\frac{29}{31}-2\frac{28}{31}\right)+\left(4-3\frac{7}{8}\right)=11\frac{1}{31}+\frac{1}{8}=11\frac{8+31}{31.8}=11\frac{39}{248}\)

a, \(\left(31\frac{6}{13}+5\frac{9}{41}\right)-36\frac{6}{13}=31\frac{6}{16}+5\frac{9}{41}-36\frac{6}{13}\)

\(=\left(31\frac{6}{16}-31\frac{6}{16}\right)+5\frac{9}{41}\)

\(=0+5\frac{9}{41}=5\frac{9}{41}\)

b, \(\left(17\frac{29}{31}-3\frac{7}{8}\right)-\left(2\frac{28}{31}-4\right)=17\frac{9}{31}-3\frac{7}{8}-2\frac{28}{31}+4\)