SOLUTION: Prove if {{{a/b = c/d = (a - c)/(b - d)}}} It's just like {{{2/4 = 1/2 = (2

SOLUTION: Prove if {{{a/b = c/d = (a - c)/(b - d)}}} It's just like {{{2/4 = 1/2 = (2 - 1)/(4-2)}}}

Question 902383: Prove if
It's just like
Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!

We need to prove that if any 2 of these

, , and  are equal, they are also
equal to the third one:

1. Prove that if , then 



Cross-multiply



Multiply both sides by -1



Add ab to both sides



Factor out a on the left.
Factor out b on the right.



Divide both sides by 

  

Cancel:



, and since ,



2. Prove that if , then 



Cross-multiply





Since ab=ba,



Subtract ab from both sides



Multiply through by -1



Divide through by bd



Cancel



, therefore



3. Prove that if , then 



Cross-multiply





Since cd=dc,



Add cd to both sides



Divide through by bd



Cancel



, therefore



Edwin

RELATED QUESTIONS
If (a+b)^2 + (b+c)^2 + (c+d)^2 = 4(ab+bc+cd), prove... (answered by mananth)

if a,b,c,d > 0 and abcd=1, prove that (1+a)(1+b)(1+c)(1+d) >=... (answered by robertb)

Prove: Q (1) [~(A�C)->Q]�Z (2) [~B v ~(A�C)]�D (3)`B->Q (4) (5) (6)... (answered by solver91311)

I have bee having trouble solving these problems and been at it for hours I need help.... (answered by solver91311)

prove validity using inference rules and rules of replacement and say which rule was used (answered by Edwin McCravy)

If a=2,b=3,c=4,d=5:solve... (answered by ValorousDawn)

(c-2b)2squared + d when a=1,b=-2, c=3, and... (answered by priya)

(a+b+c+d)^2<=4(a^2+b^2+c^2+d^2) (answered by Menjax,mathyguy)

Prove by direct proof. (use rules of interference) 1. ~ A -> (C /\ D) 2. A -> B 3. ~B (answered by solver91311)