help me

Question

1)Cho N=

$\left ( \frac{2\sqrt{x}}{\sqrt{x}+3} +\frac{\sqrt{x}}{\sqrt{x}-3}+ \frac{3x+ 3}{x-9}\right )$

$:$

$\left ( \frac{2\sqrt{x}-2 }{\sqrt{x}-3} -1\right )$

a Rút gọn N

b) Tính giá trị của N khi x = 16

2) Cho M=

$\frac{3x+3\sqrt{x}-3}{x+\sqrt{x}-2}$

$-$

$\frac{\sqrt{x}+1}{\sqrt{x}+2}$

$+$

$\frac{\sqrt{x}-2}{\sqrt{x}}$

$\left ( \frac{1}{1-\sqrt{x}}-1 \right )$

a Rút gọn M

b) tìm x để M =

$\sqrt{x}$

c) Tìm x

$\in$ N để M

$\in$ N

❄⊰๖ۣۜNgốc๖ۣۜ ⊱ ❄ · Answer 1 · 8/6/2016 11:31:49 PM

ĐK

$x> 0$

a) rútx gọn đk

$M=\frac{\sqrt{x}+1}{\sqrt{x}-1}$

b)Để

$M=\sqrt{x}\Leftrightarrow \frac{\sqrt{x}+1}{\sqrt{x}-1}=\sqrt{x}\Leftrightarrow \frac{\sqrt{x}+1}{\sqrt{x}-1}=\frac{x-\sqrt{x}}{\sqrt{x}-1}\Rightarrow \sqrt{x}+1=x-\sqrt{x}$

$\Leftrightarrow x-2\sqrt{x}-1=0$

ra z tự lm nốt nhé !!!

c)

$M=\frac{\sqrt{x}+1}{\sqrt{x}-1}=\frac{\sqrt{x}-1+2}{\sqrt{x}-1}=1+\frac{2}{\sqrt{x}-1}$

Theo bài ra :

$x\in N\Rightarrow \sqrt{x}-1\in Ư(2)$

Mà

$x>0\Rightarrow \sqrt{x}-1>-1$

Thay

+)

$\sqrt{x}-1=1\Rightarrow x=4(thoả mãn);M=3(thoả mãn )$

+)

$\sqrt{x}-1=2\Rightarrow x=9(thoả mãn );M=2(thoả mãn )$

vậy ........

~~~~~

$Amen$ ~~~~~

SherlockHolmes · Answer 2 · 8/6/2016 11:02:16 PM

Bình chọn tăng 3 Bình chọn giảm

$2.b \frac{x-\sqrt{x}+1}{\sqrt{x}-1}=\sqrt{x}$

$\Leftrightarrow x-\sqrt{x}+1=x-\sqrt{x}$

$\Leftrightarrow 1=0 \Rightarrow VN$

Trả lời 06-08-16 11:02 PM

SherlockHolmes
1

23K 20K

SherlockHolmes · Answer 3 · 8/6/2016 10:58:00 PM

Bình chọn tăng 3 Bình chọn giảm

$2) M= \frac{3x+3\sqrt{x}-3}{(\sqrt{x}-1)(\sqrt{x}+2)}-\frac{(\sqrt{x}+1)(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+2)}+\frac{(\sqrt{x}-2)(\sqrt{x}+2)(\sqrt{x}-1)}{(\sqrt{x}+2)(\sqrt{x}-1)}$

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

$=\frac{x-\sqrt{x}+1}{\sqrt{x}-1}$

Trả lời 06-08-16 10:58 PM

SherlockHolmes
1

23K 20K