Show that the given proportions are equivalent.

are u sure it's a-c/d-b for the 2nd term??

a/b=c/d

->ad=bc

a+c / b+d = a-c / b-d
->(a+c)(b-d)=(a-c)(b+d)
->ab+cb-ad-dc=ab+ad-cb-cd
->2ad=2bc
so the given proportions are equivalent

whoops did it again lol.. no its a-c / b-d ...but i still don't know how to do it

do u understand my answer??

yeah i get it.. thanks some times i have brain farts and once i see it written out im like.. oh i should have known that. thanks again!!

To show that the given proportions are equivalent, we need to prove that one proportion can be algebraically manipulated to obtain the other proportion.

Let's start with the first proportion:

(a+c) / (b+d) = (a-c) / (d-b)

To manipulate this proportion, we can cross-multiply:

(a+c) * (d-b) = (a-c) * (b+d)

Expanding both sides:

ad - ab + cd - bc = ab + ad - cb - cd

Rearranging the terms:

ad - ab - ad + cb - bc - cd = 0

We can now combine like terms:

cb - bc - cd + ad - ab - ad = 0

Simplifying further:

cb - bc - cd - ab = 0

Now, let's work with the second proportion:

a / b = c / d

To manipulate this proportion, we can cross-multiply:

a * d = b * c

Now, let's compare the two equations we have obtained:

cb - bc - cd - ab = 0 (Equation 1)
a * d = b * c (Equation 2)

Upon comparison, we can see that Equation 1 is identical to Equation 2. Therefore, we have successfully shown that the given proportions are equivalent.