Ta có : \(x^2+8x-20=\left(x-2\right)\left(x+10\right)\)

\(\left|x-2\right|=x-2\Leftrightarrow x\ge0\)

\(\left|x-2\right|=-\left(x-2\right)\Leftrightarrow x\le0\)

Vì \(x\ge0\)suy ra : \(\frac{x\left(x-2\right)}{\left(x-2\right)\left(x+10\right)}=\frac{x}{x+10}\)

Vì \(x\le0\)suy ra : \(\frac{x\left[-\left(x-2\right)\right]}{\left(x-2\right)\left(x+10\right)}=\frac{-x}{x+10}\)

chệuuu!!

Bài làm

Ta có: A = x| x-2 | / x²+ 8x - 20

A = x| x - 2 | / x² - 2x + 10x - 20

A = x| x - 2 | / x( x - 2 ) + 10( x - 2 )

A = x| x - 2 | / ( x + 10 )( x - 2 )

Nếu x ≥ 2 => x - 2 ≥ 0 => |x - 2| <=> x - 2

Nên A = x( x - 2 )/( x +10 )( x - 2 ) = x/x + 10

Nếu x ≤ 2 => x - 2 ≤ 0 => | x - 2 | = -( x - 2 )

Nên A = x.[ -( x - 2 ) ]/ ( x + 10 )( x + 2 ) = -x/ x + 10

Vậy từ biểu thức trên, ta có thể rút gọn thành hai biểu thức mới là A = x/ x + 10 và A = -x/ x +10

Do mik lm bằng đt nên k vt đc phân số. Thông cảm 

x² + 8x - 20 = x² + 10x - 2x - 20 = x(x+10) - 2(x+10) = (x - 2)(x+ 10)

|x - 2| = x - 2 nếu x > 2; |x - 2| = -(x - 2) = - x + 2 nếu x < 2

Vậy A = \(\frac{x\left(x-2\right)}{\left(x-2\right)\left(x+10\right)}=\frac{x}{x+10}\) nếu x > 2

A = \(\frac{-x\left(x-2\right)}{\left(x-2\right)\left(x+10\right)}=\frac{-x}{x+10}\) nếu x < 2

A=(x/x-2/)/x^2+8x-20=(x/x-2/)/(x-2).(x+10)

TH1:x>=2

A=x.(x-2)/(x-2).(x+10)=x/x+10

TH2:x<2

A=(-x).(x-2)/(x-2).(x+10)=-x/x+10

\(5\left(x+2\right)\left(x-2\right)-\frac{1}{2}\left(6-8x^2\right)+17\)

\(=5\left(x^2-4\right)-\left(3-4x^2\right)+17\)

\(=5x^2-20-3+4x^2+17\)

\(=9x^2-6\)

Điều kiện: x khác 0

\(=\sqrt{\frac{x^4-6x^2+9+12x^2}{x^2}}+\sqrt{x^2+4x+4-8x}\)

\(=\sqrt{\frac{x^4+6x^2+9}{x^2}}+\sqrt{x^2-4x+4}=\sqrt{\frac{\left(x^2+3\right)^2}{x^2}}+\sqrt{\left(x-2\right)^2}\)

\(=\left|\frac{x^2+3}{x}\right|+\left|x-2\right|=\frac{x^2+3}{\left|x\right|}+\left|x-2\right|\)

\(\sqrt{\frac{\left(x^2-3\right)^2+12x^2}{x^2}}+\sqrt{\left(x+2\right)^2-8x}\)

=\(\frac{\sqrt{x^4-6x+9+12x^2}}{\sqrt{x^2}}+\sqrt{x^2+4x+4-8x}\)

=\(\frac{\sqrt{x^4+6x+9}}{x}+\sqrt{x^2-4x+4}\)

=\(\frac{\sqrt{\left(x^2+3\right)^2}}{x}+\sqrt{\left(x-2\right)^2}\)

=\(\frac{\sqrt{\left(x^2+3\right)^2}}{x}+\left|x-2\right|\)

=\(\frac{x^2+3}{x}+\left|x-2\right|\)

TH1: x\(\ge\)2 =>|x-2|=x-2

=>\(\frac{x^2+3}{x}+\left|x-2\right|\)

=\(\frac{x^2+3}{x}+x-2\)

=\(\frac{x^2+3}{x}+\frac{x^2-2x}{x}=\frac{2x^2-2x+3}{x}\)

TH2:x\(\le\)2 =>|x-2|=2-x

=>\(\frac{x^2+3}{x}+\left|x-2\right|\)

=\(\frac{x^2+3}{x}+2-x\)

=\(\frac{x^2+3}{x}+\frac{2x-x^2}{x}=\frac{2x+3}{x}\)

Để \(\sqrt{x}\) xác định

 \(\Leftrightarrow x\ge0\)

\(\Leftrightarrow-7x\le0\)

\(\Rightarrow\sqrt{-7x}\)không tồn tại 

\(\Leftrightarrow\frac{8x}{4x\sqrt{x-8x}}\)không tồn tại

=> A không tồn tại 

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

b) \(\frac{x^2-16}{2x^2-8x}=\frac{\left(x-4\right)\left(x+4\right)}{2x\left(x-4\right)}=\frac{x+4}{2x}\)