Question

cho biểu thức P= \(\left(3+\dfrac{x+\sqrt{x}}{\sqrt{x+1}}\right)\left(3-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right)\)

a)tìm x để biểu thức P có nghĩa

b)Rút gọn P

Answer 1

a) ĐK: `x>=0; x \ne 1`

b) \(P=\left(3+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\right)\left(3-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right)\\ =\dfrac{3\sqrt{x}+3+x+\sqrt{x}}{\sqrt{x}+1}.\dfrac{3\sqrt{x}-3-x+\sqrt{x}}{\sqrt{x}-1}\\ =\dfrac{x+4\sqrt{x}+1}{\sqrt{x}+1}.\dfrac{-x+4\sqrt{x}-3}{\sqrt{x}-1}\\ =\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\\ =\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)=x-9\)