Ta có: \(\frac{3}{1\cdot2}+\frac{3}{3\cdot4}+\cdots+\frac{3}{299\cdot300}\)

\(=3\cdot\left(\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+\cdots+\frac{1}{299\cdot300}\right)\)

\(=3\left(1-\frac12+\frac13-\frac14+\cdots+\frac{1}{299}-\frac{1}{300}\right)\)

\(=3\cdot\left\lbrack1+\frac12+\frac13+\frac14+\cdots+\frac{1}{299}+\frac{1}{300}-2\left(\frac12+\frac14+\cdots+\frac{1}{300}\right)\right\rbrack\)

\(=3\left(1+\frac12+\frac13+\cdots+\frac{1}{300}-1-\frac12-\cdots-\frac{1}{150}\right)\)

\(=3\left(\frac{1}{151}+\frac{1}{152}+\cdots+\frac{1}{300}\right)\)

Ta có: \(\left(\frac{3}{1\cdot2}+\frac{3}{3\cdot4}+\cdots+\frac{3}{299\cdot300}\right)\cdot\left(x+\frac23\right)=\frac{2}{151}+\frac{2}{152}+\cdots+\frac{2}{300}\)

=>\(3\left(\frac{1}{151}+\frac{1}{152}+\cdots+\frac{1}{300}\right)\left(x+\frac23\right)=2\left(\frac{1}{151}+\frac{1}{152}+\cdots+\frac{1}{300}\right)\)

=>\(x+\frac23=\frac23\)

=>x=0

2/3 x X = 1/4        X x 1/5 = 1/2        X : 7/8 = 2/3

X = 1/4 : 2/3         X = 1/2 : 1/5         X = 2/3 x 7/8

X = 3/8                 X = 5/2                 X = 7/12

chúc bạn học tôt

nhanh lên các bạn tớ đang vội

Ta có: \(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{x\left(x+1\right):2}=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x\left(x+1\right)}=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=2\left(\frac{1}{2}-\frac{1}{x+1}\right)=1-\frac{2}{x+1}=\frac{2009}{2011}\)

\(\Rightarrow x=2010\).

Chúc em học tập tốt :)

ta có cái gì vậy chị huyền

a) ta có x-2/5=3/8 => x=3/8+2/5 => x=31/40

b) ta có x^2/6=24/25 => x^2=144/25 => x= +_ 12/5

c) x-1/x-5 =6/7 với x # 5) => 7(x-1)=6(x-5) => 7x-7=6x-30 => 7x-6x=6-30 => x=-24 \

nghĩ thế !

\(\dfrac{1}{3}+\dfrac{5}{6}\cdot\left(x-\dfrac{11}{5}\right)=\dfrac{3}{4}\)

\(\dfrac{5}{6}\cdot\left(x-\dfrac{11}{5}\right)=\dfrac{3}{4}-\dfrac{1}{3}\)

\(\dfrac{5}{6}\cdot\left(x-\dfrac{11}{5}\right)=\dfrac{5}{12}\)

\(x-\dfrac{11}{5}=\dfrac{5}{12}\cdot\dfrac{6}{5}\)

\(x-\dfrac{11}{5}=\dfrac{1}{2}\)

\(x=\dfrac{1}{2}+\dfrac{11}{5}\)

\(x=\dfrac{27}{10}\)

\(\dfrac{5}{6}\left(x-\dfrac{11}{5}\right)=\dfrac{3}{4}-\dfrac{1}{3}\)

\(\dfrac{5}{6}\left(x-\dfrac{11}{5}\right)=\dfrac{5}{12}\)

\(x-\dfrac{11}{5}=\dfrac{5}{12}:\dfrac{5}{6}\)

\(x-\dfrac{11}{5}=\dfrac{1}{2}\)

\(x=\dfrac{1}{2}+\dfrac{11}{5}=\dfrac{27}{10}\)

cậu 1 GTNN=1 khi x=0

câu 2 GTLN =12/11 khi x=3/2

ta co : x^2-3x+5=(x+3/2)^2+11/4  => (x+3/2)^2+11/4 >hoac= 11/4 ; roi ban lay 3 chia cho ca 2 ve ta duoc : 3/(x^2-3x+5) >hoac = 12/11 ;             dau = xay ra =>max=12/11 <=>x=-3/2                                                                                                                                                                                                     chuc ban hoc tot !!!!!

Bài 1: Ta gọi phân số cần tìm là: x(Tử số là a, mẫu số là 7)

Theo đề ta có:

\(-\frac{5}{9}< \frac{a}{7}< -\frac{2}{9}\)

\(\Rightarrow-\frac{35}{63}< \frac{9a}{63}< -\frac{14}{63}\)

=> \(-35< 9a< -14\)

Mà Từ -35 ->-14 chỉ có số: -27 và -18 chia hết cho 9 

=> \(a=\left\{-3;-2\right\}\)