\(x^2\left(x^2+4\right)-x^2-4=0\\ < =>x^2\left(x^2+4\right)-\left(x^2+4\right)=0\\ < =>\left(x^2+4\right)\left(x^2-1\right)=0\)

\(Vì :x^2\ge 0=>x^2+4\ge4>0\)

\(=>x^2-1=0\\ < =>x^2=1\\ < =>x=\pm1\)

\(Vậy :\) \(S=\left\{\pm1\right\}\)

\(\dfrac{a}{2}=\dfrac{b}{3}=>\dfrac{1}{5}.\dfrac{a}{2}=\dfrac{1}{5}.\dfrac{b}{3}=>\dfrac{a}{10}=\dfrac{b}{15}\left(1\right)\\ \dfrac{b}{5}=\dfrac{c}{4}=>\dfrac{1}{3}.\dfrac{b}{5}=\dfrac{1}{3}.\dfrac{c}{4}=>\dfrac{b}{15}=\dfrac{c}{12}\left(2\right)\)

\(\left(1\right),\left(2\right)=>\dfrac{a}{10}=\dfrac{b}{15}=\dfrac{c}{12}=\dfrac{a-b+c}{10-15+12}=\dfrac{-49}{7}=-7\\ =>a=\left(-7\right).10=-70;b=\left(-7\right).15=-105;c=\left(-7\right).12=-84\)

\(\dfrac{x-2\sqrt{xy}+y}{\sqrt{x}-\sqrt{y}}+\dfrac{x-y}{\sqrt{x}+\sqrt{y}}-\sqrt{9x}\left(x>0;y>0;x\ne y\right)\\ =\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2}{\sqrt{x}-\sqrt{y}}+\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}+\sqrt{y}}-3\sqrt{x}\\ =\sqrt{x}-\sqrt{y}+\sqrt{x}-\sqrt{y}-3\sqrt{x}\\ =-\sqrt{x}-2\sqrt{y}\)

\(\dfrac{2\sqrt{3}-3\sqrt{2}}{\sqrt{6}}-\dfrac{2-\sqrt{2}}{1-\sqrt{2}}+\dfrac{3}{\sqrt{3}}\\ =\dfrac{\sqrt{3}.\sqrt{2}.\left(\sqrt{2}-\sqrt{3}\right)}{\sqrt{6}}+\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}+\dfrac{\sqrt{3}^2}{\sqrt{3}}\\ =\sqrt{2}-\sqrt{3}+\sqrt{2}+\sqrt{3}=2\sqrt{2}\)

\(A=\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{x-1}\right):\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-1\right)\left(ĐK:x>=0;x\ne1\right)\\ =\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right):\dfrac{\sqrt{x}-\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\\ =\dfrac{\sqrt{x}+1+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\dfrac{\sqrt{x}-1}{1}\\ =\dfrac{2\sqrt{x}+1}{\sqrt{x}+1}\)

\(\dfrac{-2}{x}=\dfrac{-x}{\dfrac{8}{25}}\left(x\ne0\right)\\ =>\dfrac{2}{x}=\dfrac{x}{\dfrac{8}{25}}\\ =>x^2=2.\dfrac{8}{25}=\dfrac{16}{25}=\left(\pm\dfrac{4}{5}\right)^2\\ =>x=\pm\dfrac{4}{5}\left(TMDK\right)\)

Thỏa Mãn Điều Kiện \(x\ne0\) nha bạn.

\(3.5^x=75\\ =>5^x=\dfrac{75}{3}=25=5^2\\ =>x=2\)

\(\dfrac{x}{-15}=-\dfrac{60}{x}\left(x\ne0\right)\\ =>x^2=\left(-15\right).\left(-60\right)=900=\left(\pm30\right)^2\\ =>x=\pm30\left(TMDK\right)\)

\(ĐK:x>0;x\ne4\)

\(A=\dfrac{2\sqrt{x}}{\sqrt{x}}=2\)

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

\(P=B:A=\dfrac{\sqrt{x}-2}{\sqrt{x}}:2=\dfrac{\sqrt{x}-2}{2\sqrt{x}}\)