Question

Rút gọn biểu thức sau: 

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

Answer 1

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

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

\(=x-4+\frac{x-4}{x-4}\)

\(=x-4+1\)

\(=x-3\)

Answer 2

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

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

\(=x-4+\frac{x-4}{x-4}\)

\(=x-4+1\)

= x - 3

Answer 3

cho mình làm lại

ĐKXĐ:x khác 4

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

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

\(=\left|x-4\right|+\frac{x-4}{\left|x-4\right|}\)

+)Nếu x<4

PT trở thành \(4-x+\frac{x-4}{4-x}=4-x+\left(-1\right)=3-x\)

+)Nếu x > hoặc = 4

PT trở thành \(x-4+\frac{x-4}{x-4}=x-4+1=x-3\)

Vậy ...