Đáp án:
$9)\sqrt{x+2}-\sqrt{x-1}\\ 10)\sqrt{x+1}-\sqrt{x-2}\\ 11)\sqrt{x+2}+\sqrt{x+1}\\ 12)\sqrt{x+3}-\sqrt{x-1}$
Giải thích các bước giải:
$9)\\ \sqrt{2x+1-2\sqrt{(x-1)(x+2)}}\\ =\sqrt{x-1-2\sqrt{(x-1)(x+2)}+x+2}\\ =\sqrt{(\sqrt{x-1}-\sqrt{x+2})^2}\\ =|\sqrt{x-1}-\sqrt{x+2}|\\ =|\sqrt{x+2}-\sqrt{x-1}|\\ =\sqrt{x+2}-\sqrt{x-1}\\ 10)\\ \sqrt{2x-1-2\sqrt{x^2-x-2}}\\ =\sqrt{2x-1-2\sqrt{x^2+x-2x-2}}\\ =\sqrt{2x-1-2\sqrt{x(x+1)-2(x+1)}}\\ =\sqrt{2x-1-2\sqrt{(x-2)(x+1)}}\\ =\sqrt{x-2-2\sqrt{(x-2)(x+1)}+x+1}\\ =\sqrt{(\sqrt{x-2}-\sqrt{x+1})^2}\\ =|\sqrt{x-2}-\sqrt{x+1}|\\ =|\sqrt{x+1}-\sqrt{x-2}|\\ =\sqrt{x+1}-\sqrt{x-2}\\ 11)\\ \sqrt{2x+3+2\sqrt{x^2+3x+2}}\\ =\sqrt{2x+3+2\sqrt{x^2+x+2x+2}}\\ =\sqrt{2x+3+2\sqrt{x(x+1)+2(x+1)}}\\ =\sqrt{2x+3+2\sqrt{(x+2)(x+1)}}\\ =\sqrt{x+2+2\sqrt{(x-2)(x+1)}+x+1}\\ =\sqrt{(\sqrt{x+2}+\sqrt{x+1})^2}\\ =|\sqrt{x+2}+\sqrt{x+1}|\\ =\sqrt{x+2}+\sqrt{x+1}\\ 12)\\ \sqrt{2x+2-2\sqrt{x^2+2x-3}}\\ =\sqrt{2x+2-2\sqrt{x^2-x+3x-3}}\\ =\sqrt{2x+2-2\sqrt{x(x-1)+3(x-1)}}\\ =\sqrt{2x+2-2\sqrt{(x+3)(x-1)}}\\ =\sqrt{x+3-2\sqrt{(x-2)(x+1)}+x-1}\\ =\sqrt{(\sqrt{x+3}-\sqrt{x-1})^2}\\ =|\sqrt{x+3}-\sqrt{x-1}|\\ =\sqrt{x+3}-\sqrt{x-1}$
