主項變換數學題

1.
p = (y - ax) / ay
apy = y - ax
y - apy = ax
y(1 - ap) = ax
y = ax / (1 - ap)


2.
t = (u - 4) / (y + u)
t(y + u) = u - 4
ty + tu = u - 4
u - tu = ty + 4
u(1 - t) = ty + 4
u = (ty + 4) / (1 - t)


3.
a/c = pq - p
a = c(pq - p)
pc(q - 1) = a
p = a / [c(q - 1)]


4.
mz = (1/x) - my
my + mz = 1/x
m(y + z) = 1/x
m = 1 / x(y + z)


5.
l = e + d(n-3)
l = e + nd- 3d
nd = I + 3d - e
n = (I + 3d - e) / d


6.
(1/f) - (1/v) = (1/u)
(1/v) = (1/f) - (1/u)
(1/v) = (u - f) /uf
v = uf / (u - f)


7.
S = a(1 + r) / (1 - r)
S(1- r) = a(1 + r)
S - Sr = a + ar
Sr + ar = S - a
r(S + a) = S - a
r = (S - a) / (S + a)


8.
a(x - y) = m(x + y)
ax - ay = mx + my
ay + my = ax - mx
y(a + m) = x(a - m)
y = x(a - m) / (a + m)


9.
F = (g - h) / g
Fg = g - h
g - Fg = h
g(1 - F) = h
g = h / (1 - F)


10.
z = (x - 2y) / (y - x)
z(y- x) = x - 2y
yz - xz = x - 2y
xz + x = yz - 2y
x(z + 1) = y(z - 2)
x = y(z - 2) / (z + 1)


11.
1 + q = (p + qx) /px
px(1 + q) = p + qx
px + pqx = p + qx
px + pqx - qx = p
x(pq + p - q) = p
x = p / (pq + p - q)


12.
y = (x - b) / (x + v)
y(x + v) = x - b
xy + vy = x - b
x - xy = vy + b
x(1 - y) = vy + b
x = (vy + b) / ( 1- y)

試舉數例。

2. 我懷疑題目是 t = (u-4)/(y+u) 而非 t = u - 4/y + u

7. 我懷疑題目是 S =a(1+r)/(1-r) 而非 S =a(1+r) /1-r

12. 我懷疑題目是 y = (x-b)/(x+v) 而非 y = x - b/x + v

如果發問者不澄清（不單止以上三題，還有其他未提及的），那麼回答者有可能誤會題目，到最終也無法有效地教導發問者，那麼大家就是費時失事。

因此，發問必須清晰，表達的符號必須準確。