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\(d)8\dfrac{2}{7}-\left(3\dfrac{4}{9}+4\dfrac{2}{7}\right)\)
\(=\dfrac{8.7+2}{7}-\left(\dfrac{3.9+4}{9}+\dfrac{4.7+2}{7}\right)\)
\(=\dfrac{58}{7}-\left(\dfrac{31}{9}+\dfrac{30}{7}\right)\)
\(=\dfrac{58}{7}-\dfrac{31}{9}-\dfrac{30}{7}\)
\(=\left(\dfrac{58}{7}-\dfrac{30}{7}\right)-\dfrac{31}{9}\)
\(=\left(\dfrac{58-30}{7}\right)-\dfrac{31}{9}\)
\(=\dfrac{28}{7}-\dfrac{31}{9}\)
\(=\dfrac{28.9}{7.9}-\dfrac{31.7}{9.7}\)
\(=\dfrac{252}{63}-\dfrac{217}{63}\)
\(=\dfrac{252-217}{63}\)
\(=\dfrac{35}{63}\)
\(=\dfrac{5}{9}\)
`1+1/3=4/3`
`=>1/(1+1/3)=1:4/3=3/4`
`=>B=(1-1/3+3/4)/(1-1/3-3/4)`
`=(2/3+3/4)/(2/3-3/4)`
`=17/12:(-1/12)`
`=-17`
\(c,=\left(2\sqrt{3}-6\sqrt{2}+5\sqrt{3}\right)\sqrt{3}+5\sqrt{6}\\ =\left(7\sqrt{3}-6\sqrt{2}\right)\sqrt{3}+5\sqrt{6}\\ =21-6\sqrt{6}+5\sqrt{6}=21-\sqrt{6}\\ f,=\sqrt{\dfrac{\left(\sqrt{3}-3\right)^2}{3-\sqrt{3}}}=\sqrt{\dfrac{\left(3-\sqrt{3}\right)^2}{3-\sqrt{3}}}=\sqrt{3-\sqrt{3}}\\ i,=\dfrac{7-4\sqrt{3}+7+4\sqrt{3}}{7^2-\left(4\sqrt{3}\right)^2}=\dfrac{14}{49-48}=\dfrac{14}{1}=14\)
\(e,=2\sqrt{3\cdot2}-2\sqrt{3}\cdot3+2^2-2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2+6\sqrt{3}\\ =2\sqrt{6}-6\sqrt{3}+4-4\sqrt{3}+3+6\sqrt{3}\\ =2\sqrt{6}-4\sqrt{3}+7\)
\(=2\sqrt{3.2}-3.2\sqrt{3}+2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2+6\sqrt{3}\)
\(=2\sqrt{6}-6\sqrt{3}+4-4\sqrt{3}+3+6\sqrt{3}\)
\(=2\sqrt{6}-4\sqrt{3}+7\)
\(a,\dfrac{-13}{5}-\dfrac{-7}{15}.\dfrac{120}{63}+\dfrac{4}{5}\\ =\dfrac{-13}{5}+\dfrac{8}{9}+\dfrac{4}{5}\\ =\dfrac{-77}{45}+\dfrac{4}{5}\\ =\dfrac{-41}{45}\\ b.\left(7\dfrac{5}{9}+2\dfrac{2}{3}\right)-5\dfrac{2}{9}\\ =\left(\dfrac{68}{9}+\dfrac{8}{3}\right)-\dfrac{47}{9}\\ =\dfrac{92}{9}-\dfrac{47}{9}\\ =5\)
2)\(-\dfrac{13}{5}--\dfrac{7}{15}.\dfrac{120}{63}+\dfrac{4}{5}\)
\(=-\dfrac{13}{5}+\dfrac{7.15.8}{15.9.7}+\dfrac{4}{5}\)
\(=-\dfrac{13}{5}+\dfrac{8}{9}+\dfrac{4}{5}\)
\(=\left(-\dfrac{13}{5}+\dfrac{4}{5}\right)+\dfrac{8}{9}\)
\(=-\dfrac{9}{5}+\dfrac{8}{9}\)
\(=\dfrac{-81+40}{45}=-\dfrac{41}{45}\)
3)\(\left(7\dfrac{5}{9}+2\dfrac{2}{3}\right)-5\dfrac{2}{9}\)
\(=\left(7\dfrac{5}{9}-5\dfrac{2}{9}\right)+2\dfrac{2}{3}\)
\(=2\dfrac{1}{3}+2\dfrac{2}{3}\)
\(=5\)
d
\(\sqrt{18}-\sqrt{6}\left(\sqrt{3}-\sqrt{24}\right)\\ =\sqrt{18}-\sqrt{6.3}+\sqrt{6.24}\\ =\sqrt{18}-\sqrt{18}+\sqrt{144}\\ =0+\sqrt{12^2}\\ =12\)
e
\(\sqrt{12}\left(\sqrt{5}-\sqrt{3}\right)-\sqrt{60}\\ =\sqrt{12.5}-\sqrt{12.3}-\sqrt{60}\\ =\sqrt{60}-\sqrt{60}-\sqrt{36}\\ =0-\sqrt{6^2}\\ =0-6\\ =-6\)