F.2 simplify

1) 6ax+8ay/2ay


= a(6x+8y)/2ay-----------------------------因式分解


=6x+8y/2y


=2(3x+4y)/2y---------------------------------因式分解


=3x+4y/y


2) 12xy-8x^2/4x


= x(12y-8x)/4x---------------------------------因式分解


= 12y-8x/4x


=4 (3y-2x)/4x---------------------------------因式分解


= 3y-2x/x


3) x^3-2x^2/4-2x


=x^2(x-2)/4-2x---------------------------------因式分解


=x^2(x-2)/2(2-x)---------------------------------因式分解


=x^2(x-2)/-2(x-2)----------------------------------抽負,為了令(x-2)有得約


=x^2/-2


4) 12x^2-3/2x+1


= 3(4x^2-1)/2x+1----------------------------因式分解


=3 [(2x)^2-(1)^2]/2x+1----------------------------------------利用恆等式:(a^2-b^2)=(a-b)(a+b)


=3 (2x-1)(2x+1)/2x+1


=3(2x-1)

註:
一)因式分解時,要先在分子和分母進行因式分解


二)有時是要利用恆等式才能進行因式分解,要背熟恆等式


三)用分數來進行因解時,有時是需要約數的

1) (6ax+8ay) / 2ay
=[2a(3x+4y)] / 2ay
=(3x+4y) / 2y
2) (12xy-8x^2) / 4x
=[4x(3y-2x)] / 4x
=3y-2x
3) (x^3-2x^2) / (4-2x)
=[x^2(x-2)] / [2(2-x)]
= -(x^2) / 2
{because (2-x) x -1 = (x-2) and (x-2) x -1 = (2-x)}
4) (12x^2-3) / (2x+1)
=[3(4x^2-1)] / (2x+1)
=[3(2x-1)(2x+1)] / (2x+1)
=3(2x-1)

1.6ax+8ay/2ay
=6ax+4

2.12xy-8x^2/4x
=12xy-2x

3.x^3-2x^2/4-2x
=x^3-1/2x^2-2x

4.12x^2-3/2+1
=12x^2-1/2