a: \(\frac{9-3x}{x^2+4x-5}-\frac{x+5}{1-x}-\frac{x+1}{x+5}\)
\(=\frac{-3x+9}{\left(x+5\right)\left(x-1\right)}+\frac{x+5}{x-1}-\frac{x+1}{x+5}\)
\(=\frac{-3x+9+\left(x+5\right)^2-\left(x+1\right)\left(x-1\right)}{\left(x+5\right)\left(x-1\right)}\)
\(=\frac{-3x+9+x^2+10x+25-x^2+1}{\left(x+5\right)\left(x-1\right)}=\frac{7x+35}{\left(x+5\right)\left(x-1\right)}=\frac{7}{x-1}\)
\(B=\left(\frac{9-3x}{x^2+4x-5}-\frac{x+5}{1-x}-\frac{x+1}{x+5}\right):\frac{7x-14}{x^2-1}\)
\(=\frac{7}{x-1}\cdot\frac{x^2-1}{7\left(x-2\right)}=\frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x-2\right)}=\frac{x+1}{x-2}\)
b: \(\left(x+5\right)^2-9x-45=0\)
=>\(\left(x+5\right)^2-9\left(x+5\right)=0\)
=>(x+5)(x-4)=0
=>x=-5(loại) hoặc x=4(nhận)
Thay x=4 vào B, ta được:
\(B=\frac{4+1}{4-2}=\frac52\)
c: Để B là số nguyên thì x+1⋮x-2
=>x-2+3⋮x-2
=>3⋮x-2
=>x-2∈{1;-1;3;-3}
=>x∈{3;1;5;-1}
Kết hợp ĐKXĐ, ta được: x∈{3;-1}
d: \(B=\frac{-3}{4}\)
=>\(\frac{x+1}{x-2}=\frac{-3}{4}\)
=>4(x+1)=-3(x-2)
=>4x+4=-3x+6
=>7x=2
=>x=2/7(nhận)
e: B<0
=>\(\frac{x+1}{x-2}<0\)
=>-1<x<2
