more sat math help?

Question

If v/(v+1) x 1/V x v/(v-1)=7/w
what is w
the correct answer is 7 which would make the left side=1
so how is v/(v^2-1)=1?

what the question is saying is that the left side reduces to 1 to give u 7 for the w because 7/7=1
they didnt give me this i only found out after i got the question wrong on a practice sat
i dont understand how im supposed to get 1 on the left side thats all i want to know
as far as i know the left side reduces to v/(v^2-1)
which does not equal 1
if it did equal 1 w would equal 7
but it doesnt

if it helps they did say for positive intergers v and w but i dont see how it does

Answer 1

Ok it has been a while since I did this type of math, so I'll give it a try...

v/(v^2-1)=1
multiply boths sides by (v^2-1)
v=v^2-1
subtract v from both sides
0=v^2-v-1
here you have a simple quadratic equation. Plug it into the quadratic formula to find v.

This isn't making any sense, how can it be 7?

Answer 2

Got me. On the other hand, how would you get 7 from the equation as you show it? You can't take the v out of the w.

Answer 3

if you put one in the v the equation can not be solved