Posted by Barb on .
Show that z/pq = 1/pr + 1/qr, where r = (p + q)/z
Finding decmpositions of a fraction into 2 units as indicated on a paprus written in Greek.

Math 
Steve,
rz/pqr = q/pqr + p/pqr
rz = q + p
r = (p+q)/z 
Math 
Reiny,
RS = 1/(pr) + 1/(qr) , if r = (p+q)/z
= 1/( p(p+q)/z) + 1/( q(p+q)/z)
= z/(p(p+q)) + z/(q(p+q))
= (zq + zp)/( pq(p+q))
= z(p+q)/(pq(p+q))
= z/(p+q)
= LS
This allows you to express any fraction , which has a factorable denominator , into two fraction each with a numerator of 1
e.g.
suppose we have 5/12
5/12 = 5/(3x4)
so using the above formula
z = 5
p = 3
q=4
then r = 7/5
so 5/12 = 1/(3(7/5)) + 1/4(7/5))
= 1/(21/5) + 1/(28/5)
= 5/21 + 5/28
= 5( 1/21 + 1/28) 
Math 
Barb,
Thank you so much!!