a: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

a: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

a) ĐK: \(x\ne4,x\ne2;x\ne-2\)

b) \(A=\dfrac{x^3}{x-4}-\dfrac{x}{x-2}-\dfrac{2}{x+2}\)

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

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

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

\(A=\dfrac{x^2\left(x-1\right)-4\left(x-1\right)}{\left(x+2\right)\left(x-2\right)}\)

\(A=\dfrac{\left(x-1\right)\left(x^2-4\right)}{x^2-4}\)

\(A=x-1\)

c) \(A=0\) khi:

\(x-1=0\)

\(\Leftrightarrow x=1\left(tm\right)\)

d) A dương khi: \(A>0\)

\(x-1>0\)

\(\Leftrightarrow x>1\)

Kết hợp với đk: 

\(x>1,x\ne4,x\ne2\)

`A=(x/[x^2-4]+2/[2-x]+1/[2+x]).[x+2]/2`

`a)ĐK: x \ne +-2`

`b)` Với `x \ne +-2` có:

`A=[x-2(x+2)+x-2]/[(x-2)(x+2)].[x+2]/2`

`A=[x-2x-4+x-2]/[x-2]. 1/2`

`A=[-3]/[x-2]`

`c)x=-1` t/m đk `=>` Thay `x=-1` vào `A` có: `A=[-3]/[-1-2]=1`

dkxd  \(a\ge0,a\ne4\)

\(A=\frac{1}{\sqrt{a}+2}+\frac{1}{\sqrt{a}-2}+\frac{a}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\) 

=\(\frac{\sqrt{a}-2+\sqrt{a}+2+a}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}=\frac{a+2\sqrt{a}}{a-4}\)

A xác định khi 5x-10 ≠0 <=> X ≠ 2b) A = x²-4x+4/5x-10= (x-2)²/5(x-2)= x-2/5c) x= -2018<=> A = -2018-2/5= -2020/5 = -404

Chúc bạn học tốt

a) ĐKXĐ: \(x\ne2\)

b) Ta có: \(A=\dfrac{x^2-4x+4}{5x-10}\)

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

\(=\dfrac{x-2}{5}\)

a) ĐKXĐ: 3x + 6 khác 0

x khác -2

b) A = (x² + 4x + 4)/(3x + 6)

= (x + 2)²/[3(x + 2)]

= (x + 2)/3

c) Khi x = 1/4, ta có:

A = (1/4 + 2)/3

= (9/4)/3

= 3/4