Question

Cho B = \(\left(\sqrt{x}-\frac{x+2}{\sqrt{x}+1}\right):\left(\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{\sqrt{x}-4}{1-x}\right)\)( x ≥ 0 , x ≠ 1 , x ≠ 4 )

a, Rút gọn B

b, Tìm x để B < 0

c, Tìm x nguyên để B có giá trị nguyên

d, Tìm GTNN của B .

Các bạn ơi ! giúp mik với đi !! mai kt rồi

Answer 1

a) B=\(\left(\sqrt{x}-\frac{x+2}{\sqrt{x}+1}\right)\):\(\left(\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{\sqrt{x}-4}{1-x}\right)\)

=\(\left(\frac{x+\sqrt{x}-x-2}{\sqrt{x}+1}\right):\left(\frac{\sqrt{x}}{\sqrt{x}+1}+\frac{\sqrt{x}-4}{x-1}\right)\)

=\(\left(\frac{\sqrt{x}-2}{\sqrt{x}+1}\right):\left(\frac{\sqrt{x}}{\sqrt{x}+1}+\frac{\sqrt{x}-4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)

=\(\left(\frac{\sqrt{x}-2}{\sqrt{x}+1}\right):\left(\frac{x-\sqrt{x}+\sqrt{x}-4}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\)

=\(\frac{\sqrt{x}-2}{\sqrt{x}+1}\cdot\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{x-4}\)

=\(\frac{\sqrt{x}-2}{\sqrt{x}+1}\cdot\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)

=\(\frac{\sqrt{x}-1}{\sqrt{x}+2}\)

Vay B=\(\frac{\sqrt{x}-1}{\sqrt{x}+2}\)

b) Co B<0 ⇌ \(\frac{\sqrt{x}-1}{\sqrt{x}+2}\)<0

⇌\(\sqrt{x}-1< 0\)(vi \(\sqrt{x}+2>0\) luon dung voi x≥0)

⇌\(\sqrt{x}< 1\) ⇌ x<1 ket hop x≥0 , x≠1, x≠4

⇒ 0≤x<1

Vay 0≤x<1 thi B<0