\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}-1}{x+\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}\...">
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2 tháng 10 2018

a) \(M=\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}-1}{x+\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}\)

\(=\dfrac{\sqrt{x^3}-1^3}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{x\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}+\dfrac{x+1}{\sqrt{x}}\)

\(=\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{x\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}+\dfrac{x+1}{\sqrt{x}}\)

\(=\dfrac{x+\sqrt{x}+1}{\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}-\dfrac{x\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

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

\(=\dfrac{\left(2x+2+\sqrt{x}\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

\(=\dfrac{2x\sqrt{x}+2x+2\sqrt{x}+2+x+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

\(=\dfrac{2x\sqrt{x}+2+3\sqrt{x}+3x}{\sqrt{x}\left(\sqrt{x}+1\right)}=\dfrac{2\left(x\sqrt{x}+1\right)+3\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

\(=\dfrac{2\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)+3\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

\(=\dfrac{\left(\sqrt{x}+1\right)\left(3\sqrt{x}+2x+2\sqrt{x}+2\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

\(=\dfrac{5\sqrt{x}+2x+2}{\sqrt{x}}\)

xin lỗi bn nhé, mk chỉ bt làm đến đây thôi, k bt có đúng k

3 tháng 10 2018

nếu đề này trong sách vnen 9 trang 28 thì bạn ghi sai đề nhé

Bài 1: 

a: \(B=\dfrac{\sqrt{x}+x+\sqrt{x}-x}{1-x}\cdot\dfrac{x-1}{3-\sqrt{x}}\)

\(=\dfrac{2\sqrt{x}}{\sqrt{x}-3}\)

b: Để B=-1 thì \(2\sqrt{x}=-\sqrt{x}+3\)

=>3 căn x=3

=>căn x=1

hay x=1(loại)

a: \(M=\dfrac{x+\sqrt{x}+1-x+\sqrt{x}-1+x+1}{\sqrt{x}}=\dfrac{x+2\sqrt{x}+1}{\sqrt{x}}=\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}}\)

b: Để M=9/2 thì \(\dfrac{x+2\sqrt{x}+1}{\sqrt{x}}=\dfrac{9}{2}\)

=>2x-5 căn x+2=0

=>(căn x-2)(2 căn x-1)=0

=>x=1/4 hoặc x=4

c: \(M-4=\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}}>0\)

=>M>4

30 tháng 6 2018

có phải/....

1) \(A=\dfrac{x+3}{\sqrt{x}-2}\)

\(B=\dfrac{\sqrt{x}-1}{\sqrt{x}-2}+\dfrac{5\sqrt{x}-2}{x-4}\) hay \(B=\dfrac{\sqrt{x}-1}{\sqrt{x}-2}+\dfrac{5\left(\sqrt{x}-2\right)}{x-4}\)

2) \(A=\dfrac{\sqrt{x}+2}{\sqrt{x}+3}\)

30 tháng 6 2018

1.B=\(\dfrac{\sqrt{x-1}}{\sqrt{x+2}}\)

Bài 2: 

a: \(P=\dfrac{a-1}{2\sqrt{a}}\cdot\left(\dfrac{\sqrt{a}\left(a-2\sqrt{a}+1\right)-\sqrt{a}\left(a+2\sqrt{a}+1\right)}{a-1}\right)\)

\(=\dfrac{a-2\sqrt{a}+1-a-2\sqrt{a}-1}{2}=-2\sqrt{a}\)

b: Để P>=-2 thì P+2>=0

\(\Leftrightarrow-2\sqrt{a}+2>=0\)

=>0<=a<1

17 tháng 7 2018

\(1.a.A=\left(1-\dfrac{\sqrt{x}}{1+\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+3}{\sqrt{x}-2}+\dfrac{\sqrt{x}+2}{3-\sqrt{x}}+\dfrac{\sqrt{x}+2}{x-5\sqrt{x}+6}\right)=\dfrac{1}{\sqrt{x}+1}:\dfrac{x-9-x+4+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{1}{\sqrt{x}+1}.\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}{\sqrt{x}-3}=\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\left(x\ge0;x\ne4;x\ne9\right)\)

\(b.A< 0\Leftrightarrow\dfrac{\sqrt{x}-2}{\sqrt{x}+1}< 0\)

\(\Leftrightarrow\sqrt{x}-2< 0\)

\(\Leftrightarrow x< 4\)

Kết hợp với ĐKXĐ , ta có : \(0\le x< 4\)

KL............

\(2.\) Tương tự bài 1.

\(3a.A=\dfrac{1}{x-\sqrt{x}+1}=\dfrac{1}{x-2.\dfrac{1}{2}\sqrt{x}+\dfrac{1}{4}+\dfrac{3}{4}}=\dfrac{1}{\left(\sqrt{x}-\dfrac{1}{2}\right)^2+\dfrac{3}{4}}\le\dfrac{4}{3}\)

\(\Rightarrow A_{Max}=\dfrac{4}{3}."="\Leftrightarrow x=\dfrac{1}{4}\)

18 tháng 10 2018

Ukm ko để ý

14 tháng 10 2018

ĐỀ THI VÀO 10 ĐÓ CẢM ƠN MN TRƯỚC NHA:))

25 tháng 5 2019

a) P = \(\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}}-\frac{\sqrt{x}-1}{x+\sqrt{x}}\right)\).

P = \(\frac{\sqrt{x}.\sqrt{x}-1}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)-\sqrt{x}\left(\sqrt{x}-1\right)}\)

P = \(\frac{x-1}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{x-1-x+\sqrt{x}}\)

P = \(\frac{x-1}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)

P = \(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)

P = \(\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)

P = \(x-1\).

b) P = \(\frac{9}{2}\).

\(x-1=\frac{9}{2}\)

\(x=\frac{11}{2}\).

Vậy \(x=\frac{11}{2}\)thì P = \(\frac{9}{2}\).

25 tháng 5 2019

Thank you,bn.

Bài 2:

a: \(A=\left(5+\sqrt{5}\right)\left(\sqrt{5}-2\right)+\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{4}-\dfrac{3\sqrt{5}\left(3-\sqrt{5}\right)}{4}\)

\(=-5+3\sqrt{5}+\dfrac{5+\sqrt{5}-9\sqrt{5}+15}{4}\)

\(=-5+3\sqrt{5}+5-2\sqrt{5}=\sqrt{5}\)

b: \(B=\left(\dfrac{x+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}\right):\dfrac{x+3\sqrt{x}-2\left(\sqrt{x}+3\right)+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{x+3\sqrt{x}+6-2\sqrt{x}-6}=1\)

30 tháng 12 2022

Bài 1:

a: \(=\dfrac{x-\sqrt{x}+\sqrt{x}-3-\sqrt{x}-3}{x-9}=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)}{x-9}\)

\(=\dfrac{\sqrt{x}+2}{\sqrt{x}+3}\)

b: Để A=3/4 thì căn x+2=3

=>x=1

c: Khi x=4 thì \(A=\dfrac{2+2}{2+3}=\dfrac{4}{5}\)