\(\sqrt{18}+\sqrt{72}-5\sqrt{75}+\sqrt{12,5}\\ =\sqrt{9}.\sqrt{2}+\sqrt{36}.\sqrt{2}-5.\sqrt{25}.\sqrt{3}+\sqrt{\dfrac{25}{2}}\\ =3\sqrt{2}+6\sqrt{2}-5.5.\sqrt{3}+\dfrac{5}{\sqrt{2}}\\ =9\sqrt{2}-25\sqrt{3}+\dfrac{5\sqrt{2}}{2}\\ =\dfrac{18\sqrt{2}+5\sqrt{2}}{2}-25\sqrt{3}\\ =\dfrac{23\sqrt{2}}{2}-25\sqrt{3}\)

\(\left(a\right):\left(3x+2\right)\left(3x-2\right)-\left(3x+1\right)^2\\ =9x^2-4-\left(9x^2+6x+1\right)=-6x-5\)

\(\left(b\right):\left(1-4x^2\right)\left(1+4x^2\right)-\left(2x+3\right)^2\\ =1-16x^4-\left(4x^2+12x+9\right)\\ =-16x^4-4x^2-12x-8\)

\(\dfrac{15\times14-1}{13\times15+14}=\dfrac{15\times\left(13+1\right)-1}{15\times13+14}\\ =\dfrac{15\times13+15\times1-1}{15\times13+14}\\ =\dfrac{15\times13+14}{15\times13+14}=1\)

\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\\ =\dfrac{2.\left(\sqrt{8}-\sqrt{3}\right)}{-\sqrt{6}.\left(\sqrt{8}-\sqrt{3}\right)}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{6}.\left(\sqrt{5}+\sqrt{27}\right)}\\ =-\dfrac{2}{\sqrt{6}}-\dfrac{1}{\sqrt{6}}\\ =-\dfrac{3}{\sqrt{6}}=-\dfrac{3\sqrt{6}}{6}=-\dfrac{\sqrt{6}}{2}\)

\(\dfrac{3}{x}=\dfrac{x}{12}\left(x\ne0\right)\\ =>x^2=3.12=36=\left(\pm6\right)^2\\ =>x=\pm6\left(TMDK\right)\)

\(-17< -9< 35< 36\\ =>-\dfrac{17}{30}< -\dfrac{9}{30}< \dfrac{35}{30}< \dfrac{36}{30}\\ =>\dfrac{-17}{30}< -\dfrac{3}{10}< \dfrac{7}{6}< \dfrac{18}{15}\)

\(MSC:30\\ -\dfrac{3}{10}=\dfrac{\left(-3\right).3}{10.3}=-\dfrac{9}{30}\\ \dfrac{18}{15}=\dfrac{18.2}{15.2}=\dfrac{36}{30}\\ \dfrac{7}{6}=\dfrac{7.5}{6.5}=\dfrac{35}{30}\\ \)

\(\left(-23,57\right).\left(-28,17\right)-28,17.123,57\\ =-28,17.\left(-23,57+123,57\right)\\ =-28,17.100=-2817\)

\(\dfrac{13}{50}+9\%+\dfrac{41}{100}+0,24\\ =\dfrac{13\times2}{100}+\dfrac{9}{100}+\dfrac{41}{100}+\dfrac{24}{100}\\ =\dfrac{26+9+41+24}{100}\\ =\dfrac{100}{100}=1\)

\(\dfrac{5}{-8}+\dfrac{7}{8}=\dfrac{-5}{8}+\dfrac{7}{8}=\dfrac{-5+7}{8}=\dfrac{2}{8}=\dfrac{1}{4}\)