\(S=\frac{3}{5.7}+\frac{3}{7.9}+.....+\frac{3}{59.61}\)

\(=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+......+\frac{2}{59.61}\right)\)

=\(\frac{3}{2}.\left(\frac{7-5}{5.7}+\frac{9-7}{7.9}+......+\frac{61-59}{59.61}\right)\)

=\(\frac{3}{2}.\left(\frac{7}{5.7}-\frac{5}{5.7}+\frac{9}{7.9}-\frac{7}{7.9}+.....+\frac{61}{59.61}-\frac{59}{59.61}\right)\)

=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{59}-\frac{1}{61}\right)\)

=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)

=\(\frac{3}{2}.\frac{56}{305}\)

=\(\frac{84}{305}\)

\(\frac{23}{14}\times\frac{6}{13}-\frac{9}{14}\times\frac{6}{13}\)

\(=\frac{6}{13}\times\left(\frac{23}{14}-\frac{9}{14}\right)\)

\(=\frac{6}{13}\times1=\frac{6}{13}\)

k mk nha!

=6/13*(23/14-9/14)                                                                                                                                                                                

=6/13*14/14

=6/13*1

=6/13

`53/89 xx11/61 xx 71/37 xx 0`

`=53/89 xx11/61 xx 0`

`=53/89 xx0`

`=0`

\(\dfrac{3}{4}.\dfrac{2}{3}-\dfrac{1}{6}.\dfrac{3}{4}-\dfrac{3}{4}.\dfrac{1}{2}\) 

= \(\dfrac{3}{4}.\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\) 

= \(\dfrac{3}{4}.0\) 

= 0

\(\dfrac{3}{4}\cdot\dfrac{2}{3}-\dfrac{1}{6}\cdot\dfrac{3}{4}-\dfrac{3}{4}\cdot\dfrac{1}{2}\)

\(=\dfrac{3}{4}\left(\dfrac{2}{3}-\dfrac{1}{6}-\dfrac{1}{2}\right)\)

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

=0

\(\frac{15}{a}\cdot\frac{2}{3}\cdot\frac{3}{2}=\frac{5}{4}\)

       \(\frac{15}{a}\cdot\frac{2}{3}=\frac{5}{4}:\frac{3}{2}\)

       \(\frac{15}{a}\cdot\frac{2}{3}=\frac{5}{4}\cdot\frac{2}{3}\)

       \(\frac{15}{a}\cdot\frac{2}{3}=\frac{10}{12}\)

       \(\frac{15}{a}\cdot\frac{2}{3}=\frac{5}{6}\)

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

              \(\frac{15}{a}=\frac{5}{6}\cdot\frac{3}{2}\)

              \(\frac{15}{a}=\frac{15}{12}\)

Ta có: \(\frac{15}{a}=\frac{15}{12}\) 

Mặt khác: 15 = 15 => a = 12

Vậy a tìm được bằng 12

\(\frac{3}{4}+\frac{5}{9}:\frac{4}{5}=\frac{3}{4}+\frac{5}{9}\times\frac{5}{4}\)

\(=\frac{3}{4}+\frac{25}{36}=\frac{27}{36}+\frac{25}{36}=\frac{27+25}{36}=\frac{52}{36}=\frac{13}{9}\)

\(\frac{7}{19}\times\frac{4}{7}-\frac{7}{19}\times\frac{3}{7}=\frac{7}{19}\times\left(\frac{4}{7}-\frac{3}{7}\right)\)

\(=\frac{7}{19}\times\frac{1}{7}=\frac{1}{19}\)

a. \(\frac{3}{4}+\frac{5}{9}\div\frac{4}{5}=\frac{3}{4}+\frac{25}{36}=\frac{13}{9}.\)

b. \(\frac{7}{19}\times\frac{4}{7}-\frac{7}{19}\times\frac{3}{7}=\frac{7}{19}\times\left(\frac{4}{7}-\frac{3}{7}\right)=\frac{7}{19}\times\frac{1}{7}=\frac{1}{19}\)