公式主項的變換,救命丫.好吾明><就考試..

提醒你 : 做方程式要用天秤的原理, 左邊和右邊要永遠相同.
另, 盡量將主項移到左邊, 其他項則移到右邊.

1) 1/a - 1/b = 1/c [b]
_____- 1/b = 1/c - 1/a (左右同時減以 1/a)
______1/b = - 1/c + 1/a (左右同時乘以 -1)
_________= (c - a)/ac (右邊通分母)
_______b = ac/(c - a) (左右同時被 1 除)

2) F = (g - 1)/g [g]
__Fg = g - 1 (左右同時乘以 g)
Fg - g = -1 (左右同時減以 g)
g(F - 1) = -1 (左邊抽公因數 g)
____g = -1/(F - 1) (左右同時除以 (F - 1))
_____= 1/(1 - F) (右邊上下同時乘以 -1)

3) 1/y = (1/x) + c [x]
1/y - 1/x = c (左右同時減以 1/x)
___-1/x = c - 1/y (左右同時減以 1/y)
______= (cy - 1)/y (右邊通分母)
____1/x = (1 - cy)/y (左右同時乘以 -1)
_____x = y/(1 - cy) (左右同時被 1 除)

4) (a - b)x - (a + b)y = 0 [a]
___ax - bx - ay - by = 0 (展開左邊)
__a(x - y) - b(x + y) = 0 (左邊重組並抽公因數 a 和 b)
_________a(x - y) = b(x + y) (左右同時加以 [b(x + y)])
______________a = b(x + y)/(x - y) (左右同時除以 (x - y))

5) y = (a + bx)/(c + dx) [x]
y(c + dx) = a + bx (左右同時乘以 (c + dx))
yc + dxy = a + bx (展開左邊)
yc + dxy - bx = a (左右同時減以 bx)
dxy - bx = a - yc (左右同時減以 yc)
x(dy - b) = a - yc (左邊抽公因數 x)
______x = (a - yc)/(dy - b) (左右同時除以 (dy - b))

6) t = n / [2(T-10)H] [T]
t(T - 10) = n / (2H) (左右同時乘以 (T - 10))
__T - 10 = n / (2Ht) (左右同時除以 t)
_____T = [n / (2Ht)] + 10 (左右同時加以 10)

7) X = (1-y)/(1+y) [y]
X(1 + y) = 1 - y (左右同時乘以 (1 + y))
X + Xy = 1 - y (展開左邊)
X + Xy + y = 1 (左右同時加以 y)
Xy + y = 1 - X (左右同時減以 X)
y(X + 1) = 1 - X (左邊抽公因數 y)
____y = (1 - X)/(X + 1) (左右同時除以 (X + 1))

希望這樣可以幫到你溫習.

Q1)
1/a - 1/b = 1/c [b]
1/a - 1/c = 1/b
(c-a) / ac = 1/b
b( c-a ) = ac
b = ac / (c-a)

Q2)
F = (g-1) /g [g]
F = g/g - 1/g
F = 1 - 1/g
1/g = 1 - F
1 = g( 1-F )
g = 1 / ( 1-F )

Q3)
1/y = (1/x) + c [x]
1/y - c = 1/x
1/y - cy/y = 1/x
( 1-cy ) / y = 1/x
x( 1-cy ) = y
x = y / ( 1-cy )

Q4)
(a-b)x - (a+b)y = 0 [a]
ax - bx - ay - by = 0
a(x-y) - b(x+y) = 0
a(x-y) = b(x+y)
a = b(x+y) / (x-y)

Q5)
y = (a+bx) / (c+dx) [x]
y(c+dx) = a + bx
yc + ydx = a + bx
ydx - bx = a - yc
x( yd-b ) = a - yc
x = (a-yc) / (yd-b)

Q6)
t = n / 2(T-10)H [T]
(T-10)t = n / 2H
(T-10) = n / 2Ht
T = 10 + ( n / 2Ht )

Q7)
X = (1-y)/(1+y) [y]
X(1+y) = 1 - y
X + Xy = 1 - y
Xy + y = 1 - X
y(X + 1) = 1-X
y = (1-X)/(1+X)