F.2代數分式&公式(20點)

1) Find the L.C.M. of 10x、15x
5x)10x , 15x.... 2 , 3
LCM = 5x (2) (3) = 30x

2) Find the L.C.M. of 12y , 8(y+1) and 6y(y+1)
2y)12y , 8(y+1) , 6y(y+1).....6 , 4(y+1) , 3(y+1)
LCM = 2y (6) [4(y+1)] [3(y+1)] = 144y(y+1)^2

3) Simplify 21x^2 y^5 / 14x^6 y^3
(21x^2y^5) / (14x^6y^3)
= (3y^2) / (2x^4)

4) Simplify 4x - 8y / x^2 - 2xy
(4x-8y) / (x^2-2xy)
= [4(x-2y)] / [x(x-2y)]
= 4 / x

5) Simplify 2a - 2b / bx-ax
(2a-2b) / (bx-ax)
= [2(a-b)] / [-x(a-b)]
= 2 / -x
= -2 / x

6) Simplify 2r + 2s / r^2 × rx^3 / rx + sx
[(2r+2s)/r^2] x [(rx^3)/(rx+sx)]
= [2(r+s)/r^2] x {(rx^3)/[x(r+s)]
= [2(r+s)(rx^3)] / [r^2x(r+s)]
= (2x^2) / r

7) Simplify ms-ns / ms^2 ÷ m^2 - mm / ms
係咪抄錯問題???

8) Simplify 2/1 + 1/3m
2/1 ??? 係咪抄錯問題???

9) Simplify 3 / x-y + 1 / y-x
3/(x-y) + 1/(y-x)
= 3/(x-y) - 1/(x-y)
= (3-1) / (x-y)
= 2 / (x-y)

10) Simplify 2 / 3( a+b ) + 5 / 2(a+b)
[2/3(a+b)] + [5/2(a+b)]
= [2(2)]/[2(3)(a+b)] + [5(3)]/[3(2)(a+b)]
= (4+15) / [6(a+b)]
= 19 / [6(a+b)]

2008-11-06 21:11:23 補充：
11) Simplify 2 / x-3 + 1 / x - 6
[2/(x-3)] + [1/(x-6)]
= [2(x-6)+(x-3)] / [(x-3)(x-6)]
= (2x-12+x-3) / [(x-3)(x-6)]
=(3x-15) / [(x-3)(x-6)]
= [3(x-5)] / [(x-3)(x-6)]

12) Make x the subject of the formula y = ax + b
y = ax+b
y-b = ax
x = (y-b)/a

2008-11-06 21:11:40 補充：
13) Make r the subject of the formula P = 4( 1- rs )
P=4(1-rs)
P/4=1-rs
rs=1-(P/4)
r=[1-(P/4)]/s

14) If 5p - 7 = 3( p+q ) , express p in terms of q .
5p-7 = 3(p+q)
5p-7 = 3p+3q
5p-3p = 3q+7
2p = 3q+7
p= (3q+7)/2

2008-11-06 21:11:53 補充：
15) Make t the subject of the formula F = 2( t-1 ) / m
F = [2(t-1)]/m
Fm = 2(t-1)
[Fm/2] = t+1
t = (Fm/2)-1

16) Make m the subject of the formula A =mx + 3my + 5nz
A = mx+3my+5nz
A-5nz = mx+3my
A-5nz = m(x+3y)
m= (A-5nz)/(x+3y)

2008-11-06 21:12:11 補充：
17) Make x the subject of the formula y = x-2 / x+1
y = (x-2) / (x+1)
y(x+1) = x-2
xy+y = x-2
y+2 = x-xy
y+2 = x(1-y)
x = (y+2) / (1-y)

2008-11-06 21:12:21 補充：
18) Make r the subject of the formula s = 2+r / r-7
s = (2+r) / (r-7)
s(r-7) = 2+r
sr-7s = 2+r
sr-r = 2+7s
r(s-1) = 2+7s
r = (2+7s)/(s-1)

19) Make x the subject of the formula y = a + b/2x
y = a+(b/2x)
y-a = b/(2x)
x = b/[2(y-a)]

2008-11-06 21:12:34 補充：
20) It is known that if the temperature of the ground is G , then the
temperature T at h m above the ground can be found using the
formula T = G - 1 / 100 h .
a) Make h the subject of the above formula .
T = G-(1/100h)
1/(100h) = G-T
h = 1/[100(G-T)]

2008-11-06 21:12:46 補充：
20b) If the temperature at the foot of the Mountain Everext is 30 , what
is the altitude of the mountain at which the snow starts to form .
(Assume snow will form when the temperature decrease to 0 )
Sub. T = 0 and G = 30 into result of (a)
h = 1/[100(30-0)]
= 1/[100(30)]
= 1/3000

12) x = ( y-b ) / a
13) r = ( P-4 ) / (-4s)
14) p = (3q+7)/2
15) t = (Fm + 2) /2
16) m = (A - 5nz) / (x+3y)
17) x = (y+2)/(1-y)
18) r = (2+s7) / (s-1)
19) x = (a+b) / 2y