\(B=\left(\dfrac{4}{1-\sqrt{5}}+\dfrac{1}{2+\sqrt{5}}-\dfrac{4}{3-\sqrt{5}}\right)\left(\sqrt{5}-6\right)\)

\(B=\left[\dfrac{4\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)}+\dfrac{2-\sqrt{5}}{\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)}-\dfrac{4\left(3+\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}\right]\left(\sqrt{5}-6\right)\)

\(B=\left[\dfrac{4\left(1+\sqrt{5}\right)}{1-5}+\dfrac{2-\sqrt{5}}{4-5}-\dfrac{4\left(3+\sqrt{5}\right)}{9-5}\right]\left(\sqrt{5}-6\right)\)

\(B=\left[-\dfrac{4\left(1+\sqrt{5}\right)}{4}-\dfrac{2-\sqrt{5}}{1}-\dfrac{4\left(3+\sqrt{5}\right)}{4}\right]\left(\sqrt{5}-6\right)\)

\(B=\left(-1-\sqrt{5}-2+\sqrt{5}-3-\sqrt{5}\right)\left(\sqrt{5}-6\right)\)

\(B=\left(-\sqrt{5}-6\right)\left(\sqrt{5}-6\right)\)

\(B=-\left(\sqrt{5}+6\right)\left(\sqrt{5}-6\right)\)

\(B=-\left(5-36\right)\)

\(B=-\left(-31\right)\)

\(B=31\)

_____________________________

\(\sqrt{48}-\dfrac{\sqrt{21}-\sqrt{15}}{\sqrt{7}-\sqrt{5}}+\dfrac{2}{\sqrt{3}+1}\)

\(=4\sqrt{3}-\dfrac{\sqrt{3}\left(\sqrt{7}-\sqrt{5}\right)}{\sqrt{7}-\sqrt{5}}+\dfrac{2\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)

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

\(=3\sqrt{3}-\sqrt{3}+1\)

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

\(\dfrac{-5}{8}-\dfrac{1}{3}+\dfrac{7}{-6}=\dfrac{-5}{8}-\dfrac{1}{3}-\dfrac{7}{6}=\dfrac{-15}{24}-\dfrac{8}{24}-\dfrac{28}{24}=\dfrac{-51}{24}=\dfrac{-17}{8}\)

\(\dfrac{-5}{8}-\dfrac{1}{3}+\dfrac{7}{-6}=\dfrac{-17}{8}\)

\(\dfrac{-17}{8}\)

`(6-2 4/5)*3 1/8-1 3/5:1/4`

`=(6-14/5)*25/8-8/5*4`

`=16/5*25/8-32/5`

`=10-32/5=18/5`

=(30/5-14/5).25/8.4

=16/5.25/2

=8.5/1.1

=40

\(a,\dfrac{-8}{15}+\dfrac{13}{30}-\dfrac{5}{12}=\dfrac{-32}{60}+\dfrac{26}{60}-\dfrac{25}{60}=-\dfrac{31}{60}\\ b,\dfrac{3}{2}.\dfrac{7}{2}+\left(\dfrac{-5}{6}+\dfrac{1}{10}:\dfrac{11}{30}\right)=\dfrac{21}{4}+\left(\dfrac{-5}{6}+\dfrac{3}{11}\right)=\dfrac{21}{4}+\dfrac{-37}{66}=\dfrac{619}{132}\)

\(c,\dfrac{-20}{21}.\dfrac{22}{35}+\dfrac{-20}{21}.\dfrac{13}{35}+\dfrac{-22}{21}=\dfrac{-20}{21}\left(\dfrac{22}{35}+\dfrac{13}{35}\right)+\dfrac{-22}{21}=\dfrac{-20}{21}.1+\dfrac{-22}{21}=\dfrac{-20}{21}+\dfrac{-22}{21}=\dfrac{-42}{21}=-2\)

\(a,\left(31\dfrac{6}{13}+5\dfrac{9}{41}\right)-36\dfrac{6}{13}\\ =\left(31-36\right)+\left(\dfrac{6}{13}-\dfrac{6}{13}\right)+5\dfrac{9}{41}\\ =-5+0+5\dfrac{9}{41}\\ =\left(-5+5\right)+\dfrac{9}{41}=\dfrac{9}{41}\)

\(b,\dfrac{5}{3}+\left(-\dfrac{2}{7}\right)-\left(-1,2\right)\\ =\dfrac{5}{3}-\dfrac{2}{7}+\dfrac{6}{5}\\ =\dfrac{5.35-2.15+6.21}{105}=\dfrac{271}{105}\\ c,0,25+\dfrac{3}{5}-\left(\dfrac{1}{8}-\dfrac{2}{5}+1\dfrac{1}{4}\right)=\dfrac{1}{4}+\dfrac{3}{5}-\dfrac{1}{8}+\dfrac{2}{5}-1\dfrac{1}{4}\\ =\left(-1\dfrac{1}{4}+\dfrac{1}{4}\right)+\left(\dfrac{3}{5}+\dfrac{2}{5}\right)-\dfrac{1}{8}=-1+1-\dfrac{1}{8}=-\dfrac{1}{8}\)

a) (31 6/13 + 5 9/41) - 36 6/13

= 409/13 + 214/41 - 474/13

= (409/13 - 474/13) + 214/41

= -5 + 214/41

= 9/41

b) 5/3 + (-2/7) - (-1,2)

= 5/3 - 2/7 + 6/5

= 29/21 + 6/5

= 271/105

c) 0,25 + 3/5 - (1/8 - 2/5 + 1 1/4)

= 1/4 + 3/5 - 1/8 + 2/5 - 5/4

= (1/4 - 5/4) + (3/5 + 2/5) - 1/8

= -1 + 1 - 1/8

= -1/8

a)\(\dfrac{19}{48}-\dfrac{3}{40}=\dfrac{95}{240}-\dfrac{18}{240}=\dfrac{77}{240}\)

b)\(\dfrac{1}{6}+\dfrac{7}{27}+\dfrac{5}{18}=\dfrac{9}{54}+\dfrac{14}{54}+\dfrac{15}{54}=\dfrac{38}{54}=\dfrac{19}{27}\)

a) 19/48 - 3/40= 77/240

b) 1/6 + 7/27 + 5/18= 23/54 + 5/18= 19/27

a)\(\dfrac{19}{48}\) - \(\dfrac{3}{40}\)=\(\dfrac{77}{240}\)

b) \(\dfrac{1}{6}\)+\(\dfrac{7}{27}\)+\(\dfrac{5}{18}\)=\(\dfrac{23}{54}\)+\(\dfrac{5}{18}\)=\(\dfrac{19}{27}\)

\(A=\left(7-\dfrac{3}{4}+\dfrac{1}{3}\right)-\left(6+\dfrac{5}{4}-\dfrac{4}{3}\right)-\left(5-\dfrac{7}{4}+\dfrac{5}{3}\right)\)

\(\Rightarrow A=7-\dfrac{3}{4}+\dfrac{1}{3}-6-\dfrac{5}{4}+\dfrac{4}{3}-5+\dfrac{7}{4}-\dfrac{5}{3}\)

\(\Rightarrow A=\left(7-6-5\right)-\dfrac{3}{4}-\dfrac{5}{4}+\dfrac{7}{4}+\dfrac{1}{3}+\dfrac{4}{3}-\dfrac{5}{3}\)

\(\Rightarrow A=-4-\dfrac{1}{4}+0\)

\(\Rightarrow A=-\dfrac{17}{4}\)

Cách 2 tính trong dấu ngoặc đơn của A, bạn tự tính nhé.

A = -17/4

A = -17/4

\(a,\dfrac{15^3}{5^4}\)

\(=\dfrac{\left(3\cdot5\right)^3}{5^4}\)

\(=\dfrac{3^3\cdot5^3}{5^4}\)

\(=\dfrac{3^3}{5}\)

\(=\dfrac{27}{5}\)

\(---\)

\(b,\dfrac{21^3}{7^4}\)

\(=\dfrac{\left(3\cdot7\right)^3}{7^4}\)

\(=\dfrac{3^3\cdot7^3}{7^4}\)

\(=\dfrac{3^3}{7}\)

\(=\dfrac{27}{7}\)

\(---\)

\(c,\dfrac{6^6}{3^8}\)

\(=\dfrac{\left(2\cdot3\right)^6}{3^8}\)

\(=\dfrac{2^6\cdot3^6}{3^8}\)

\(=\dfrac{2^6}{3^2}\)

\(=\dfrac{64}{9}\)

#\(Toru\)

a) $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$   ;    $\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

Vậy $\frac{1}{2} \times \frac{1}{3} = \frac{1}{3} \times \frac{1}{2}$

$\frac{3}{5} \times \frac{1}{6} = \frac{3}{{30}} = \frac{1}{{10}}$  ;    $\frac{1}{6} \times \frac{3}{5} = \frac{3}{{30}} = \frac{1}{{10}}$

Vậy $\frac{3}{5} \times \frac{1}{6} = \frac{1}{6} \times \frac{3}{5}$

b) Học sinh tự thực hiện