a: (x-1)(x-4)=0
=>x=1(nhận) hoặc x=4(loại)
Khi x=1 thì \(A=\frac{1^2-1}{1-4}=0\)
b: \(B=\frac{x+1}{x+4}-\frac{6}{4-x}-\frac{24}{x^2-16}\)
\(=\frac{x+1}{x+4}+\frac{6}{x-4}-\frac{24}{\left(x+4\right)\left(x-4\right)}\)
\(=\frac{\left(x+1\right)\left(x-4\right)+6\left(x+4\right)-24}{\left(x-4\right)\left(x+4\right)}\)
\(=\frac{x^2-3x-4+6x+24-24}{\left(x-4\right)\left(x+4\right)}=\frac{x^2+3x-4}{\left(x-4\right)\left(x+4\right)}\)
\(=\frac{\left(x+4\right)\left(x-1\right)}{\left(x-4\right)\left(x+4\right)}=\frac{x-1}{x-4}\)
c: A=B
=>\(\frac{x-1}{x-4}=\frac{x^2-x}{x-4}\)
=>\(x^2-x=x-1\)
=>\(x^2-2x+1=0\)
=>\(\left(x-1\right)^2=0\)
=>x=1(nhận)
