Question

giúp mik nha

Answer 1

\(A=\sqrt{\dfrac{\left(x-5\right)^4}{\left(4-x\right)^2}}-\dfrac{x^2-25}{x-4}\)

\(A=\sqrt{\dfrac{\left(x-5\right)^4}{\left(x-4\right)^2}}-\dfrac{x^2-25}{x-4}\) (do \(\left[A\left(x\right)\right]^2=\left[-A\left(x\right)\right]^2\))

\(A=\dfrac{\left(x-5\right)^2}{x-4}-\dfrac{x^2-25}{x-4}\)

\(A=\dfrac{\left(x-5\right)^2-x^2-25}{x-4}\)

\(A=\dfrac{x^2-10x+5^2-x^2-25}{x-4}\)

\(A=\dfrac{-10x}{x-4}\)

Vậy \(A=\dfrac{-10x}{x-4}\)

Chúc bạn học tốt!!!

Answer 2

ĐIỀU KHIỆN \(x\ne4\)

A = \(\sqrt{\dfrac{\left(x-5\right)^4}{\left(4-x\right)^2}}-\dfrac{x^2-25}{x-4}\) = \(\sqrt{\dfrac{\left(\left(x-5\right)^2\right)^2}{\left(4-x\right)^2}}+\dfrac{x^2-25}{4-x}\)

= \(\dfrac{x^2-10x+25}{4-x}+\dfrac{x^2-25}{4-x}\) (vì \(x< 4\))

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

Answer 3

A = \(\sqrt{\dfrac{\left[\left(x-5\right)^2\right]^2}{\left(4-x\right)^2}}+\dfrac{\left(x-5\right)\left(x+5\right)}{4-x}\)

A = \(\dfrac{\left(x-5\right)^2}{4-x}+\dfrac{\left(x-5\right)\left(x+5\right)}{4-x}\)

A = \(\dfrac{\left(x-5\right)\left(x-5+x+5\right)}{4-x}\)

A = \(\dfrac{2x\left(x-5\right)}{4-x}\)

P/s: Ko biết có sai ko nx :P