f.2 數學(快.20分)

1. F=g-1/g {g}

Fg=g-1
Fg-g=-1
g(F-1)=-1
g=-1/(F-1)

2. y=ax+b/bx {b}

ybx=ax+b
ybx-b=ax
b(yx-1)=ax
b=(ax)/(yx-1)

3. R-7= aR-2rs/4r {r]

4r(R-7)=aR-2rs
4rR-28r=aR-2rs
4rR-4r7+2rs=aR
r(4R-28+2s)=aR
r=(aR)/(4R-28+2s)

4. a=2b/b+1 {b}

a(b+1)=2b
ab+a=2b
ab-2b=-a
b(a-2)=-a
b=-a/(a-2)


5. D=b(36L+5)/24L-M {L]

D(24L-M)=b(36L+5)
24DL-DM=36Lb+5b
24DL-36Lb=5b+DM
L(24D-36b)=5b+DM
L=(5b+DM)/(24D-36D)

6. P=(3V-RT/4T+V)-1 {T}
P+1=3V-RT/4T+V
(P+1)(4T+V)=3V-RT
4TP+PV+4T+V=3V-RT
4TP+4T+RT=3V-PV-V
T(4P+4+R)=V(2-P)
T=[V(2-P)]/(4P+4+R)

solve for x

7. ax-bc/d=e

ax-bc=ed
ax=ed+bc
x=(ed+bc)/a

8.ax-bx=cd

x(a-b)=cd
x=cd/(a-b)

9.(ax-b/x) -d=e

ax-b/x=e+d
ax-b=ex+dx
ax-ex-dx=b
x(a-e-d)=b
x=b/(a-e-d)

10. p(x+q)=q(x-p)

px+pq=qx-pq
px-qx=-pq-pq
x(p-q)=-2pq
x=-2pq/(p-q)

7. ax-bc/d=e

AX - BC = DE
AX = DE + BC
X = DE+BC / A

8.ax-bx=cd

X ( A - B ) = CD
X = CD / ( A - B )

9.(ax-b/x) -d=e

AX-B / X = E+D
AX-B = EX+DX
AX-EX+DX = B
X ( A-E+D ) = B
X = B / ( A-E+D)

10. p(x+q)=q(x-p)

PX + PQ = QX - PQ
PX -QX = - PQ - PQ
X ( P -Q ) = - PQ - PQ
- X ( P - Q ) = PQ + PQ
- X ( P - Q ) = 2PQ
- X = 2PQ / ( P - Q )
X = -2PQ / ( P + Q )

7. ax-bc/d=e

ax-bc=ed
x =(ed+bc) / a

8.ax-bx=cd
(a-b)x=cd
x=cd / (a-b)

10. p(x+q)=q(x-p)
px+pq=qx-pq
x(p-q)=-2pq
x=-2pq / (p-q)