ok 

\(a,ĐK:x\ne0;x\ne-5\\ b,A=\dfrac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}\\ A=\dfrac{x^2+4x-5}{2\left(x+5\right)}=\dfrac{\left(x+5\right)\left(x-1\right)}{2\left(x+5\right)}=\dfrac{x-1}{2}\\ c,A=1\Leftrightarrow x-1=2\Leftrightarrow x=3\left(tm\right)\)

\(A=\dfrac{x^2+2x}{2\left(x+5\right)}+\dfrac{x-5}{x}+\dfrac{50-5x}{2x\left(x+5\right)}\\ ĐKXĐ:\left\{{}\begin{matrix}x\ne0\\x+5\ne0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ne0\\x\ne-5\end{matrix}\right.\)

ĐKXĐ: \(x\ne-5;0\)

\(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x.\left(x+5\right)}\)

\(=\frac{\left(x^2+2x\right).x}{2x.\left(x+5\right)}+\frac{2.\left(x+5\right).\left(x-5\right)}{2x.\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+2x^2}{2x\left(x+5\right)}+\frac{2.\left(x^2-25\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}=\frac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}\)

\(=\frac{x^3+4x^2-5x}{2x\left(x+5\right)}=\frac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}=\frac{x\left(x+5\right)\left(x-1\right)}{2x\left(x+5\right)}=\frac{x-1}{2}\)

b. \(A=0\Leftrightarrow\frac{x-1}{2}=0\Rightarrow x-1=0\Leftrightarrow x=1\)

\(A=\frac{1}{4}\Leftrightarrow\frac{x-1}{2}=\frac{1}{4}\Leftrightarrow4x-4=2\Leftrightarrow4x-6=0\Leftrightarrow x=\frac{3}{2}\)

c. Với x=0 thì \(A=\frac{0-1}{2}=-\frac{1}{2}\)

Với  x=2 thì: \(A=\frac{2-1}{2}=\frac{1}{2}\)

d. \(A>0\Leftrightarrow\frac{x-1}{2}>0\Rightarrow\left(x-1\right).2>0\Rightarrow x-1>0\Leftrightarrow x>1\)

\(A< 0\Leftrightarrow\frac{x-1}{2}< 0\Leftrightarrow\left(x-1\right).2< 0\Leftrightarrow x-1< 0\Leftrightarrow x< 1;x\ne-5,0\)

e. \(A=\frac{x-1}{2}\inℤ\Rightarrow x-1\in Z\Rightarrow x\inℤ\)

Và \(\left(x-1\right)⋮2\Rightarrow x:2dư1\)

Vậy \(A\in Z\Leftrightarrow x\inℤ\)và x chia 2 dư 1

d. Bổ sung x khác -5 nữa nhé

A, Để biểu thức A có nghĩa thì 

\(2x+10\ne0\Rightarrow x\ne-5\)

\(x\ne0\)

\(2x^2+10x\ne0\Rightarrow x\ne0;x\ne-5\)

Vậy điều kiện của x là \(x\ne0;x\ne-5\)

b) Ta có:

\(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x^2+10x}\)

\(A=\frac{x\cdot\left(x^2+2x\right)+\left(x-5\right)\cdot\left(2x+10\right)+50-5x}{2x^2+10x}\)

\(A=\frac{x^3+4x^2-5x}{2x^2+10x}\)

\(A=\frac{x\cdot\left(x-1\right)\cdot\left(x+5\right)}{2x\cdot\left(x+5\right)}\)

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

Để A=1 thì ta có\(\frac{x-2}{2}=1\Leftrightarrow x-2=2\Leftrightarrow x=4\)

Vậy x=4 thì A=1

a: ĐKXĐ: \(x\notin\left\{0;-5\right\}\)

Nhìn mãi mới hiểu cái đề bài @-@

`a)đk:` $\begin{cases}\sqrt{x^2-2x} \ge 0\\x+\sqrt{x^2-2x} \ne 0\\x-\sqrt{x^2-2x} ne 0\\\end{cases}$
`<=>` $\begin{cases}x \ge 2\,or\,x<0\\x \ne 0\end{cases}$
`b)A=(x+sqrt{x^2-2x})/(x-sqrt{x^2-2x})-(x-sqrt{x^2-2x})/(x+sqrt{x^2+2x})`
`=((x+sqrt{x^2-2x})^2-(x-sqrt{x^2-2x})^2)/((x+sqrt{x^2-2x})(x-sqrt{x^2-2x}))`
`=(x^2+x^2-2x+2sqrt{x^2-2x}-x^2-x^2+2x+2sqrt{x^2-2x})/(x^2-x^2+2x)`
`=(4sqrt{x^2-2x})/(2x)`
`=(2sqrt{x^2-2x})/x`
`c)A<2`
`<=>2sqrt{x^2-2x}<2x`
`<=>sqrt{x^2-2x}<x(x>=2)`(BP 2 vế thì x>=2)
`<=>x^2-2x<x^2`
`<=>2x>0`
`<=>x>0`
`<=>x>=2`
Vậy `x>=2` thì `A<2`.

bài 1 :

tự làm

a: ĐKXĐ: \(x\notin\left\{0;-5\right\}\)

b: \(\Leftrightarrow2n^2+n-2n-1+3⋮2n+1\)

\(\Leftrightarrow2n+1\in\left\{1;-1;3;-3\right\}\)

hay \(n\in\left\{0;-1;1;-2\right\}\)

a) ĐKXĐ: \(x\notin\left\{0;-5\right\}\)

Ta có: \(B=\dfrac{x^2+2x}{2x+10}+\dfrac{x-5}{x}-\dfrac{5x-50}{2x^2+10x}\)

\(=\dfrac{x^2+2x}{2\left(x+5\right)}+\dfrac{x-5}{x}-\dfrac{5x-50}{2x\left(x+5\right)}\)

\(=\dfrac{x^3+2x^2}{2x\left(x+5\right)}+\dfrac{2\left(x+5\right)\left(x-5\right)}{2x\left(x+5\right)}-\dfrac{5x-50}{2x\left(x+5\right)}\)

\(=\dfrac{x^3+2x^2+2x^2-50-5x+50}{2x\left(x+5\right)}\)

\(=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}\)

\(=\dfrac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}\)

\(=\dfrac{x^2+5x-x-5}{2\left(x+5\right)}\)

\(=\dfrac{x\left(x+5\right)-\left(x+5\right)}{2\left(x+5\right)}\)

\(=\dfrac{\left(x+5\right)\left(x-1\right)}{2\left(x+5\right)}\)

\(=\dfrac{x-1}{2}\)

b) Để B=0 thì \(\dfrac{x-1}{2}=0\)

\(\Leftrightarrow x-1=0\)

hay x=1(nhận)

Vậy: Để B=0 thì x=1

Để \(B=\dfrac{1}{4}\) thì \(\dfrac{x-1}{2}=\dfrac{1}{4}\)

\(\Leftrightarrow4\left(x-1\right)=2\)

\(\Leftrightarrow4x-4=2\)

\(\Leftrightarrow4x=6\)

hay \(x=\dfrac{3}{2}\)(nhận)

Vậy: Để \(B=\dfrac{1}{4}\) thì \(x=\dfrac{3}{2}\)

c) Thay x=3 vào biểu thức \(B=\dfrac{x-1}{2}\), ta được:

\(B=\dfrac{3-1}{2}=\dfrac{2}{2}=1\)

Vậy: Khi x=3 thì B=1

d) Để B<0 thì \(\dfrac{x-1}{2}< 0\)

\(\Leftrightarrow x-1< 0\)

\(\Leftrightarrow x< 1\)

Kết hợp ĐKXĐ, ta được: 

\(\left\{{}\begin{matrix}x< 1\\x\notin\left\{0;-5\right\}\end{matrix}\right.\)

Vậy: Để B<0 thì \(\left\{{}\begin{matrix}x< 1\\x\notin\left\{0;-5\right\}\end{matrix}\right.\)

Để B>0 thì \(\dfrac{x-1}{2}>0\)

\(\Leftrightarrow x-1>0\)

hay x>1

Kết hợp ĐKXĐ, ta được: x>1

Vậy: Để B>0 thì x>1