a) \(A=\dfrac{\sqrt[]{x}+2}{\sqrt[]{x}-5}\) có nghĩa \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt[]{x}-5\ne0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\sqrt[]{x}\ne5\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne25\end{matrix}\right.\)

Khi \(x=16\Rightarrow A=\dfrac{\sqrt[]{16}+2}{\sqrt[]{16}-5}=\dfrac{4+2}{4-5}=-6\)

b) \(B=\dfrac{3}{\sqrt[]{x}+5}+\dfrac{20-2\sqrt[]{x}}{x-25}\)

B có nghĩa \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x-25\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne25\end{matrix}\right.\)

\(\Leftrightarrow B=\dfrac{3\left(\sqrt[]{x}-5\right)+20-2\sqrt[]{x}}{\left(\sqrt[]{x}+5\right)\left(\sqrt[]{x}-5\right)}\)

\(\Leftrightarrow B=\dfrac{3\sqrt[]{x}-15+20-2\sqrt[]{x}}{\left(\sqrt[]{x}+5\right)\left(\sqrt[]{x}-5\right)}\)

\(\Leftrightarrow B=\dfrac{\sqrt[]{x}+5}{\left(\sqrt[]{x}+5\right)\left(\sqrt[]{x}-5\right)}\)

\(\Leftrightarrow B=\dfrac{1}{\sqrt[]{x}-5}\left(dpcm\right)\)

c) \(A=\dfrac{\sqrt[]{x}+2}{\sqrt[]{x}-5}\in Z\left(x\in Z\right)\)

\(\Leftrightarrow\sqrt[]{x}+2⋮\sqrt[]{x}-5\)

\(\Leftrightarrow\sqrt[]{x}+2-\left(\sqrt[]{x}-5\right)⋮\sqrt[]{x}-5\)

\(\Leftrightarrow\sqrt[]{x}+2-\sqrt[]{x}+5⋮\sqrt[]{x}-5\)

\(\Leftrightarrow7⋮\sqrt[]{x}-5\)

\(\Leftrightarrow\sqrt[]{x}-5\in U\left(7\right)=\left\{-1;1;-7;7\right\}\)

\(\Leftrightarrow x\in\left\{16;36;144\right\}\)

d) \(A>B\left(2\sqrt[]{x}+5\right)\)

\(\Leftrightarrow\dfrac{\sqrt[]{x}+2}{\sqrt[]{x}-5}>\dfrac{1}{\sqrt[]{x}-5}\left(2\sqrt[]{x}+5\right)\)

\(\Leftrightarrow\sqrt[]{x}+2>2\sqrt[]{x}+5\)

\(\Leftrightarrow\sqrt[]{x}< -3\)

mà \(\sqrt[]{x}\ge0\)

\(\Leftrightarrow x\in\varnothing\)

Nếu là câu c 

c, Ta có : BD là phân giác \(\widehat{ABC}\)

\(\Rightarrow\dfrac{AD}{DC}=\dfrac{AB}{BC}\left(1\right)\)

Ta có : BK là phân giác \(\widehat{ABH}\)

\(\Rightarrow\dfrac{HK}{AK}=\dfrac{BH}{AB}\left(2\right)\)

Ta có: ΔHBA ~ ΔABC (cmt ) 

^{(*nếu chưa c/m tam giác đồng dạng thì hãy c/m,  làm r thì khỏi )}

\(\Rightarrow\dfrac{HB}{AB}=\dfrac{AB}{AC}\left(3\right)\)

\(\left(1\right)\left(2\right)\left(3\right)\Rightarrow\dfrac{AD}{DC}=\dfrac{HK}{AK}\)

\(\Rightarrow AK.AD=HK.CD\left(đpcm\right)\)

giúp mình câu c câu d với

c: (x-2)^2+2(2-x)=0

=>(x-2)^2-2(x-2)=0

=>(x-2)(x-4)=0

=>x=2 hoặc x=4

c: ĐKXĐ: x<>8

\(\dfrac{3}{2x-16}+\dfrac{3x-20}{x-8}+\dfrac{1}{8}=\dfrac{13x-102}{3x-24}\)

=>\(\dfrac{9}{6\left(x-8\right)}+\dfrac{18x-120}{6\left(x-8\right)}-\dfrac{26x-204}{6\left(x-8\right)}=\dfrac{-1}{8}\)

=>\(\dfrac{18x-111-26x+204}{6\left(x-8\right)}=\dfrac{-1}{8}\)

=>\(\dfrac{-8x+93}{6x-48}=\dfrac{-1}{8}\)

=>\(\dfrac{8x-93}{6x-48}=\dfrac{1}{8}\)

=>8(8x-93)=6x-48

=>64x-744-6x+48=0

=>58x=696

=>x=12

d: ĐKXĐ: x<>1; x<>-1

\(\dfrac{6}{x^2-1}+5=\dfrac{8x-1}{4x+4}+\dfrac{12x-1}{4x-4}\)

=>\(\dfrac{24}{4\left(x-1\right)\left(x+1\right)}+\dfrac{20\left(x^2-1\right)}{4\left(x-1\right)\left(x+1\right)}=\dfrac{\left(8x-1\right)\left(x-1\right)+\left(12x-1\right)\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)}\)

=>8x^2-9x+1+12x^2+12x-x-1=24+20x^2-20

=>20x^2+2x=20x^2+4

=>2x=4

=>x=2(loại)