gusterguy said:
If v/v+1 x 1/v x v/v-1 = 7/w for positive integers v and w, what is the value of w?
Are you sure you're supposed to "simplify" (from your subject line), rather than solve for the value(s) of w...? :?:
If the former, I'm afraid I'm not sure how to proceed. If the latter, then I will first assume that you mean the following:
. . . . .[ v / (v + 1) ] * [ 1 / v ] * [ v / (v - 1) ] = 7 / w
....rather than the "(v/v) + (1x)(1/v)(xv)/v - 1 = 7/w" that you posted. If this is correct, then, noting first that clearly v cannot equal -1, 0, or 1 (why?), you can multiply the left-hand side to get:
. . . . .v / ( v[sup:114bk7u1]2[/sup:114bk7u1] - 1 ) = 7 / w
. . . . .vw = 7v[sup:114bk7u1]2[/sup:114bk7u1] - 7
. . . . .w = 7v - (7/v)
Since w must be a whole number (or its negative), then 7v - (7/v) must be also. Since v is an integer, then clearly so is 7v. This means that, for w to take on a valid value, 7/v must be a whole number.
What values then can v take on? What are the corresponding values of w?
Eliz.
