f.2 maths......

1. 12x(y+z)^2+24x2(y+z)+6x(y+z)^2
=12(y+z)^2+48(y+z)+6(y+z)^2
=6(y+z)[2(y+z)+8+(y+z)]
=6(y+z)[2y+2z+8+y+z]
=6(y+z)(3y+3z+8)

2.a)
x=1/(n+1)
nx+x=1
nx=1-x
n=(1-x) / x

b)
y=n/(n-1)
ny-y=n
ny-n=y
n(y-1)=y
n=y /(y-1)

c)
(1-x) / x = y /(y-1) from(a),(b)
(1-x)(y-1)=xy
y-1-xy+x=xy--------(1)
2xy-y=x-1
y(2x-1)=x-1
y=(x-1) / (2x-1)

d)
y-1-xy+x=xy from(1)
2xy-x=y-1
x(2y-1)=y-1
x=(y-1) / (2y-1)

1.因式分解
12x(y+z)^2+24x2(y+z)+6x(y+z)^2
=12(y+z)^2+48(y+z)+6(y+z)^2
=6(y+z)[2(y+z)+8+(y+z)]
=6(y+z)[2y+2z+8+y+z]
=6(y+z)(3y+3z+8)

2.x=1/n+1和y=n/n-1
a.試以x表示n
x=1/n+1
x-1=1/n
n=1/x-1

b.試以y表示n
y=n/n-1
ny-y=n
ny-n=y
n(y-1)=y
n=y/y-1

c.試以x表示y
y/y-1=1/x-1
xy-y=y-1
xy-2y=-1
y(x-2)=-1
y=-1/x-2

d.試以y表示x
y/y-1=1/x-1
xy-y=y-1
x=2y-1/y