Đáp án:
$a)\dfrac{x^3}{|x|}\\ b)4x$
Giải thích các bước giải:
$a)\dfrac{x^3}{y^2}:\sqrt{\dfrac{x^2}{y^4}}\\ =\dfrac{x^3}{y^2}.\sqrt{\dfrac{y^4}{x^2}}\\ =\dfrac{x^3}{y^2}.\dfrac{y^2}{|x|}\\ =\dfrac{x^3}{|x|}\\ b)\sqrt{\dfrac{27(x-1)^2}{12}}+\dfrac{3}{2}-(x-2)\sqrt{\dfrac{50x^2}{8(x-2)^2}}\\ =\sqrt{\dfrac{9(x-1)^2}{4}}+\dfrac{3}{2}-(x-2)\sqrt{\dfrac{25x^2}{4(x-2)^2}}\\ =\dfrac{3|x-1|}{2}+\dfrac{3}{2}-(x-2).\dfrac{5|x|}{2|x-2|}\\ =\dfrac{3(x-1)}{2}+\dfrac{3}{2}+(x-2).\dfrac{5x}{2(x-2)}\\ =\dfrac{3(x-1)}{2}+\dfrac{3}{2}+\dfrac{5x}{2}\\ =\dfrac{3(x-1)+3+5x}{2}\\ =\dfrac{8x}{2}\\ =4x$
