Bài 149:
a: Để A nguyên thì \(x^3-5x^2+2x^2-10x-x+5+3⋮x-5\)
\(\Leftrightarrow x-5\in\left\{1;-1;3;-3\right\}\)
hay \(x\in\left\{6;4;8;2\right\}\)
b: Để B nguyên thì \(x+8\in\left\{1;-1;67;-67\right\}\)
hay \(x\in\left\{-7;-9;59;-75\right\}\)
Bài 148
Ta có (x + y/x^2 - xy + 1/y - x) : (y^2/x^2 - y^2 + y/x + y)
Ta có x + y/x^2 - xy + 1/y - x = x + y/x.(x - y) + 1/y - x
= -x - y/x.(y - x) + x/x.(y - x)
= -x - y + x/x.(y - x) = -y/x.(y - x) (1)
Ta có y^2/x^2 - y^2 + y/x + y = y^2/(x - y)(x + y) + y/x + y
= y^2/(x - y)(x + y) + y(x - y)/(x + y)(x - y)
= y^2 + y(x - y)/(x + y)(x - y) = y^2 + xy/(x + y)(x - y) (2)
Từ (1) và (2), ta có
VT = -y/x.(y - x) : y^2 + xy/(x + y)(x - y)
= -y/x.(y - x) . (x + y)(x - y)/y^2 + xy
= y/x.(x - y) . (x + y)(x - y)/y^2 + xy
= y/x . x + y/y^2 + xy
= 1/x . x + y/x + y = 1/x = 1.(x^2 - y^2)/x.(x^2 - y^2)
= x^2 - y^2/x^3 - y^2x (đpcm)