Question 1098557

in general, the reciprocal of a is equal to 1/a and the reciprocal of a/b is equal to b/a.


in the expression of 1 / (xy), the reciprocal is equal to (xy) / 1, which is equal to (xy).


in the expression of (2f-v) / (fv), the reciprocal is equal to  (fv) / (2f-v).


you can confirm by assigning arbitrary values to the variables to see if the basic concept of a reciprocal being 1 divided by the expression holds true.


in the expression of 1 / (xy), if you let x = 2 and y = 3, the expression becomes 1 / 6.


the reciprocal should be 1 / (1/6) which is equal to 6.


x * y is the reciprocal and is equal to 2 * 3 which is equal to 6, so the concept of reciprocality holds.


in the expression of (2f-v) / (fv), if you let f = 2 and v = 3, then the expression becomes (2*2-3) / (2*3) which is equal to 1/6.


the reciprocal of 1/6 is equal to 6.


(fv) / (2f-v) is equal to (2*3) / (2*2-3) which is equal to 6/1 which is equal to 6.


the concept of reciprocality holds here as well.


the reciprocal of any expression is 1 divided by that expression.


the rest is just mathematical manipulation to get it to look like what you want.


for example, you can say that the reciprocal of (a/b) / (c/d) is equal to (c/d) / (a/b), but how did you get there?


the reciprocal of (a/b) / (c/d) is equal to 1 / ((a/b) / (c/d))


your numerator is 1 and your denominator is (a/b) / (c/d).


multiply both numerator and denominator by (c/d) and:


your numerator becomes 1 * (c/d) which is equal to (c/d).


your denominator becomes (a/b) / (c/d) * (c/d) which is equal to (a/b).


your expression becomes (c/d) / (a/b).


reciprocal of (a/b) / (c/d) is (c/d) / a/b), all derived from the fact that:


the reciprocal of (a/b) / (c/d) is equal to 1 divided by (a/b) / (c/d).


note that when you multiply the numerator of an expression and the denominator of an expression by the same amount, the value of the expression remains the same.


example:


3/6 * 5/5 = 15/30 which is the same as 3/6 which is the same as 1/2.