Thực hiện các phép tính sau:
a) 2x2−1x−2+−x2−3x−22x2−1x−2+−x2−3x−2
b) xx+y+yx−yxx+y+yx−y
c) 1x−1−2x2−11x−1−2x2−1
d) x+2x2+xy−y−2xy+y2x+2x2+xy−y−2xy+y2
e) 12x2−3x−14x2−912x2−3x−14x2−9
g) 2x9−x2+1x−3−1x+32x9−x2+1x−3−1x+3
Sử dụng quy tắc cộng, trừ phân thức
a)
2x2−1x−2+−x2−3x−22x2−1x−2+−x2−3x−2
=x2−4x−2=x2−4x−2
=(x−2)(x+2)x−2=x+2
Advertisements (Quảng cáo)
b)
xx+y+yx−y
=x(x−y)(x+y)(x−y)+y(x+y)(x−y)(x+y)=x2−xy+xy+y2(x−y)(x+y)=x2+y2x2−y2
c)
1x−1−2x2−1=x+1(x−1)(x+1)−2(x−1)(x+1)=x−1(x−1)(x+1)=1x+1
d)
x+2x2+xy−y−2xy+y2
=x+2x(x+y)−y−2y(x+y)=(x+2)yxy(x+y)−(y−2)xxy(x+y)=xy+2yxy(x+y)−xy−2xxy(x+y)=2y+2xxy(x+y)=2(x+y)xy(x+y)=2xy
e)
12x2−3x−14x2−9
=1x(2x−3)−1(2x−3)(2x+3)=2x+3x(2x−3)(2x+3)−xx(2x−3)(2x+3)=x+3x(4x2−9)
g)
2x9−x2+1x−3−1x+3
=−2x(x−3)(x+3)+1x−3−1x+3=−2x(x−3)(x+3)+x+3(x−3)(x+3)−x−3(x−3)(x+3)=−2x+6(x−3)(x+3)=−2(x−3)(x−3)(x+3)=−2x+3