1. \(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)

= \(\frac{5}{9}\) .(\(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\) )

= \(\frac{5}{9}\) . 1 = \(\frac{5}{9}\)

a) x+ \(\frac{4}{5}\)= \(\frac{4}{5}\)+ ( \(\frac{3}{7}\)+ \(\frac{3}{5}\))

    x + \(\frac{4}{5}\)=  \(\frac{4}{5}\)+ \(\frac{36}{35}\)

    => x = \(\frac{36}{35}\)

Vậy : x = \(\frac{36}{35}\)

b) \(\frac{4}{9}\)+\(\frac{8}{9}\)+ \(\frac{12}{9}\)+ ... + \(\frac{56}{9}\)

    = \(\frac{4+8+12+...+56}{9}\)

    Ta có : 4+8+12 + ... +56

     Số các số hạng của dẫy số trên là : ( 56 -4) + 4 +1 = 14 ( số hạng )

      => Tổng trên = ( 4+56) x 14 : 2 = 420

      => \(\frac{4}{9}\)+ \(\frac{8}{9}\)+ ... + \(\frac{56}{9}\)= \(\frac{420}{9}\)= \(\frac{140}{3}\)

a)x=3/7+3/5=3x(1/7+1/5)=36/35

b)=(4+8+...+56)/9=(56+4)x14/9=280/3
 

a)

\(\begin{array}{l}\frac{{13}}{{23}}.\frac{7}{{11}} + \frac{{10}}{{23}}.\frac{7}{{11}}\\ = \frac{7}{{11}}.\left( {\frac{{13}}{{23}} + \frac{{10}}{{23}}} \right)\\ = \frac{7}{{11}}.\frac{23}{23}\\ = \frac{7}{{11}}.1\\ = \frac{7}{{11}}\end{array}\)                                   

b)

\(\begin{array}{l}\frac{5}{9}.\frac{{23}}{{11}} - \frac{1}{{11}}.\frac{5}{9} + \frac{5}{9}\\ = \frac{5}{9}.\left( {\frac{{23}}{{11}} - \frac{1}{{11}} + 1} \right)\\ = \frac{5}{9}.\left( {2 + 1} \right)\\ = \frac{5}{9}.3 = \frac{5}{3}\end{array}\)

c)

\(\begin{array}{l}\left[ {\left( { - \frac{4}{9} + \frac{3}{5}} \right):\frac{{13}}{{17}}} \right] + \left( {\frac{2}{5} - \frac{5}{9}} \right):\frac{{13}}{{17}}\\ = \left( { - \frac{4}{9} + \frac{3}{5}} \right).\frac{{17}}{{13}} + \left( {\frac{2}{5} - \frac{5}{9}} \right).\frac{{17}}{{13}}\\ = \frac{{17}}{{13}}.\left( { - \frac{4}{9} + \frac{3}{5} + \frac{2}{5} - \frac{5}{9}} \right)\\ = \frac{{17}}{{13}}.\left[ {\left( { - \frac{4}{9} - \frac{5}{9}} \right) + \left( {\frac{3}{5} + \frac{2}{5}} \right)} \right]\\ =\frac{{17}}{{13}}. (\frac{-9}{9}+\frac{5}{5})\\= \frac{{17}}{{13}}.\left( { - 1 + 1} \right)\\ = \frac{{17}}{{13}}.0 = 0\end{array}\)          

d)

\(\begin{array}{l}\frac{3}{{16}}:\left( {\frac{3}{{22}} - \frac{3}{{11}}} \right) + \frac{3}{{16}}:\left( {\frac{1}{{10}} - \frac{2}{5}} \right)\\ = \frac{3}{{16}}:\left( {\frac{3}{{22}} - \frac{6}{{22}}} \right) + \frac{3}{{16}}:\left( {\frac{1}{{10}} - \frac{4}{{10}}} \right)\\ = \frac{3}{{16}}:\frac{{ - 3}}{{22}} + \frac{3}{{16}}:\frac{{ - 3}}{{10}}\\ = \frac{3}{{16}}.\frac{{ - 22}}{3} + \frac{3}{{16}}.\frac{{ - 10}}{3}\\ = \frac{3}{{16}}.\left( {\frac{{ - 22}}{3} + \frac{{ - 10}}{3}} \right)\\ = \frac{3}{{16}}.\frac{{ - 32}}{3}\\ =  - 2\end{array}\)

giúp với ạ

giải dc nhưng mà hoi lâu

a)\(\dfrac{5}{7}+\dfrac{4}{9}=\dfrac{45}{63}+\dfrac{28}{63}=\dfrac{73}{63}\) ; \(\dfrac{9}{11}+\dfrac{3}{8}=\dfrac{72}{88}+\dfrac{33}{88}=\dfrac{105}{88}\)

\(\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{2}{15}\); \(\dfrac{16}{25}-\dfrac{2}{5}=\dfrac{16}{25}-\dfrac{10}{25}=\dfrac{6}{25}\)

a)\(\frac{11^4.6-11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5+9^8.7}\)

\(=1.6:\frac{9^8.3-9^8.9}{9^8.\left(5+7\right)}\)

\(=6:\frac{9^8.\left(3-9\right)}{9^8.12}\)

\(=6:\frac{9^8.\left(-6\right)}{9^8.12}\)

\(=6:\left(-\frac{6}{12}\right)\)

\(=6:\left(-\frac{1}{2}\right)\)

\(=-12\)

b) 3/5 : ( -1/5-1/6)+3/5:(-1/3-16/15) ( mình chuyển về ps luôn )

=3/5: (-11/30) + 3/5 : (-7/5) 

=3/5:[-11/30+(-7/5)]

=3/5:53/30

=18/53

c) (1/2-13/14):5/7-(-2/21+1/7):5/7

= -3/7:5/7-1/21:5/7

=(-3/7-1/21):5/7

=-10/21:5/7

=-2/3

câu b vá c mình làm tắt nha. chúc bạn học tốt

a. \(\frac{2}{3}+\frac{1}{3}.\left(\frac{-4}{9}+\frac{5}{6}\right):\frac{7}{12}\)

\(=1.\frac{7}{12}:\frac{7}{12}\)

\(=1\)

b. 

\(\frac{5}{9}.\frac{8}{11}+\frac{5}{9}.\frac{9}{11}-\frac{5}{9}.\frac{6}{11}\)

\(=\frac{5}{9}.\left(\frac{8}{11}+\frac{9}{11}-\frac{6}{11}\right)\)

\(=\frac{5}{9}.1\)

\(=\frac{5}{9}\)

Tk mk nha!

b)  \(=\frac{5}{9}.\left(\frac{8}{11}+\frac{9}{11}-\frac{6}{11}\right)\)

\(=\frac{5}{9}.1\)

\(=\frac{5}{9}\)

a,\(=\frac{2}{3}+\left(\frac{-4}{27}+\frac{5}{18}\right):\frac{7}{12}\)=\(\frac{2}{3}+\frac{-16}{63}+\frac{10}{21}\)=\(\frac{8}{9}\)

\(\frac{11}{9}.\frac{15}{4}-\frac{11}{4}.\frac{7}{9}-\frac{11}{9}.\frac{5}{4}\)

=\(\frac{11}{9}.\frac{15}{4}-\frac{11}{9}.\frac{7}{4}-\frac{11}{9}.\frac{5}{4}\)

=\(\frac{11}{9}\).\(\left(\frac{15}{4}-\frac{7}{4}-\frac{5}{4}\right)\)

=\(\frac{11}{9}\).\(\frac{3}{4}\)

=\(\frac{11.3}{3.3.4}\)

=\(\frac{11}{12}\)

Chúc bn học tốt

Trả lời:

\(\frac{11}{9}.\frac{15}{4}-\frac{11}{4}.\frac{7}{9}-\frac{11}{9}.\frac{5}{4}\)

\(=\frac{11}{9}.\left(\frac{15}{4}-\frac{7}{4}-\frac{5}{4}\right)\)

\(=\frac{11}{9}.\frac{3}{4}\)

\(=\frac{11}{12}\)

Hok tốt!

Vuong Dong Yet

11/9 . 15/4 - 11/4 . 7/9 - 11/9 . 5/4

= 11/9 . ( 15/4 - 7/4 - 5/4 )

= 11/9 . 3/4

= 11/12

\(F=\frac{5}{9}+\frac{4}{9}\cdot\frac{3}{7}+\frac{4}{9}\cdot\frac{4}{7}\)

\(F=\frac{5}{9}+\frac{4}{9}\cdot\left(\frac{3}{7}+\frac{4}{7}\right)\)

\(F=\frac{5}{9}+\frac{4}{9}\cdot1\)

'\(F=\frac{5}{9}+\frac{4}{9}\)

\(F=1\)