Question

Rút gọn:

\(\sqrt{\frac{\left(x-5\right)^4}{\left(4-x\right)^2}}-\frac{x^2-25}{x-4}\)

Answer 1

ĐKXĐ: \(x\ne4\)

Ta có: \(\sqrt{\frac{\left(x-5\right)^4}{\left(4-x\right)^2}}-\frac{x^2-25}{x-4}\)

\(=\frac{\left(x-5\right)^2}{\left|x-4\right|}-\frac{x^2-25}{x-4}\)(*)

Trường hợp 1: x>4

(*)\(=\frac{\left(x-5\right)^2-x^2+25}{x-4}=\frac{x^2-10x+25-x^2+25}{x-4}\)

\(=\frac{-10x+50}{x-4}\)

Trường hợp 2: x<4

(*)\(=\frac{\left(x-5\right)^2}{4-x}-\frac{x^2-25}{x-4}\)

\(=\frac{x^2-10x+25}{4-x}+\frac{x^2-25}{4-x}\)

\(=\frac{x^2-10x+25+x^2-25}{4-x}\)

\(=\frac{2x^2-10x}{4-x}\)