Câu 1:
1: \(2xy^2-4y\)
\(=2y\cdot xy-2y\cdot2\)
=2y(xy-2)
2: \(x^2y-6xy+9y\)
\(=y\cdot\left(x^2-6x+9\right)\)
\(=y\left(x-3\right)^2\)
3: \(x^2+x-y^2-y\)
\(=\left(x^2-y^2\right)+\left(x-y\right)\)
=(x-y)(x+y)+(x-y)
=(x-y)(x+y+1)
4: \(x^2+4x+3\)
\(=x^2+x+3x+3\)
=x(x+1)+3(x+1)
=(x+1)(x+3)
bài 3:
a: \(P=\frac{2x^2-1}{x^2+x}-\frac{x-1}{x}+\frac{3}{x+1}\)
\(=\frac{2x^2-1-\left(x-1\right)\left(x+1\right)+3x}{x\left(x+1\right)}\)
\(=\frac{2x^2+3x-1-x^2+1}{x\left(x+1\right)}=\frac{x^2+3x}{x\left(x+1\right)}=\frac{x+3}{x+1}\)
b: P=0
=>\(\frac{x+3}{x+1}=0\)
=>x+3=0
=>x=-3
c: \(x^2-x=0\)
=>x(x-1)=0
=>x=0(loại) hoặc x=1(nhận)
Khi x=1 thì \(P=\frac{1+3}{1+1}=\frac42=2\)
