vì 0<x,y,z\(\le\)1 nên (1-x)(1-y) >=0 <=> 1+xy >= x+y

<=> 1+z+xy >= x+y+z

<=> \(\frac{y}{1+z+xy}\le\frac{y}{x+y+z}\left(1\right)\)

tương tự có \(\frac{x}{1+y+xz}\le\frac{x}{x+y+z}\left(2\right);\frac{z}{1+x+xy}\le\frac{z}{x+y+z}\left(3\right)\)

cộng theo vế của (1), (2), (3) ta được

\(\frac{x}{1+y+xz}+\frac{y}{1+z+xy}+\frac{z}{1+x+yz}\le\frac{x+y+z}{x+y+z}\le\frac{3}{x+y+z}\)

dấu "=" xảy ra khi x=y=z=1

\(\frac{x}{1+y+zx}+\frac{y}{1+z+xy}+\frac{z}{1+x+yz}\le\text{Σ}\frac{x}{x^2+xy+zx}=\text{Σ}\frac{x}{x\left(x+y+z\right)}=\frac{3}{x+y+z}\)

Do \(1\ge x^2\)và \(y\ge xy\)

Dấu = xảy ra khi x = y = z = 1

1, \(\frac{1}{2}-\left(6\frac{5}{9}+x-\frac{117}{8}\right):\left(12\frac{1}{9}\right)=0\)

   \(\left(\frac{6.9+5}{9}+x-\frac{117}{8}\right):\frac{12.9+1}{9}=\frac{1}{2}\)

 ( . là nhân nha) 

    \(\left(\frac{59}{9}-\frac{117}{8}+x\right):\frac{109}{9}=\frac{1}{2}\)

    \(\frac{59}{9}-\frac{117}{8}+x=\frac{1}{2}\cdot\frac{109}{9}\)

    \(\frac{59}{9}-\frac{117}{8}+x=\frac{109}{18}\)

   \(x=\frac{109}{18}-\frac{59}{9}+\frac{117}{8}\)

\(x=\frac{113}{8}\)

( \(\left(y+\frac{1}{3}\right)+\left(y+\frac{2}{9}\right)+\left(y+\frac{1}{27}\right)+\left(y+\frac{1}{81}\right)=\frac{56}{81}\)

   \(y+\frac{1}{3}+y+\frac{2}{9}+y+\frac{1}{27}+y+\frac{1}{81}=\frac{56}{81}\)

\(4y+\frac{1}{3}+\frac{2}{9}+\frac{1}{27}+\frac{1}{81}=\frac{56}{81}\)

\(4y+\frac{49}{81}=\frac{56}{81}\)

\(4y=\frac{7}{81}\)

y      =  7/81:4

y       = 7/324

Giúp mk đi.

câu a để sau

b) x = 3; y = 5

874

90

\(x:3\frac{5}{6}=2\frac{8}{15}\)

\(x:\frac{23}{5}=\frac{38}{15}\)

        \(x=\frac{38}{15}.\frac{23}{5}\)

         \(x=\frac{874}{75}\)

X=3 ; Y =5 đó bạn

Còn về trả lời thỉ mk ko bt đâu .Mò đấy!

x=1/5

y=1/3

\(x+\frac{15}{7}=\frac{9}{2}\)

\(x=\frac{9}{2}-\frac{15}{7}=\frac{33}{14}\)

\(x-\frac{3}{4}=\frac{7}{2}\)

\(x=\frac{7}{2}+\frac{3}{4}=\frac{17}{4}\)

\(x.\frac{7}{8}=\frac{12}{5}\)

\(x=\frac{12}{5}:\frac{7}{8}=\frac{96}{35}\)

\(\frac{5}{6}:x=\frac{4}{3}\)

\(x=\frac{5}{6}:\frac{4}{3}=\frac{5}{8}\)

• a) x=9/2-15/7=33/14
• b) x=7/2+3/4=17/4
• c) x=12/5:7/8=61/35
• d) x=5/6:4/3=5/8
• k nha

a) \(\frac{11}{15}+\frac{5}{7}+\frac{2}{7}+\frac{4}{15}=\left(\frac{11}{15}+\frac{4}{15}\right)+\left(\frac{5}{7}+\frac{2}{7}\right)\)

\(=2\)

b) \(\frac{5}{9}\times\frac{1}{2}\times\frac{5}{9}\times\frac{6}{4}=\frac{25}{81}\times\frac{3}{4}=\frac{25}{108}\)

c) \(\frac{7}{8}\div\frac{1}{2}+\frac{9}{8}\div\frac{1}{2}=\left(\frac{7}{8}+\frac{9}{8}\right)\div\frac{1}{2}\)

\(=2\div\frac{1}{2}=4\)

d) \(\frac{17}{10}+\frac{1}{2}-\frac{7}{10}=\left(\frac{17}{10}-\frac{7}{10}\right)+\frac{1}{2}\)

\(=1+\frac{1}{2}=\frac{3}{2}\)

a) \(\frac{11}{15}+\frac{5}{7}+\frac{2}{7}+\frac{4}{15}\)

\(=\left(\frac{11}{15}+\frac{4}{15}\right)+\left(\frac{5}{7}+\frac{2}{7}\right)\)

\(=1+1\)

\(=2\)

b) \(\frac{5}{9}.\frac{1}{2}.\frac{5}{9}.\frac{6}{4}\)

\(=\left(\frac{5}{9}\right)^2\left(\frac{1}{2}.\frac{6}{4}\right)\)

\(=\frac{25}{81}.\frac{3}{4}\)

\(=\frac{25}{108}\)

c) \(\frac{7}{8}:\frac{1}{2}+\frac{9}{8}:\frac{1}{2}\)

\(=\frac{7}{8}.2+\frac{9}{8}.2\)

\(=2\left(\frac{7}{8}+\frac{9}{8}\right)\)

\(=2.\frac{16}{8}\)

\(=2.2\)

\(=4\)

d) \(\frac{17}{10}+\frac{1}{2}-\frac{7}{10}\)

\(=\left(\frac{17}{10}-\frac{7}{10}\right)+\frac{1}{2}\)

\(=1+\frac{1}{2}\)

\(=\frac{2}{2}+\frac{1}{2}\)

\(=\frac{3}{2}\)