Question

if x/a=y/b=z/c,show that xz+ac/xz-ac=yz+bc/yz-bc ​

Answer 1

Given :   x/a=y/b=z/c  

To find : Show that (xz+ac)/(xz-ac)=(yz+bc)/(yz-bc)

Solution:

Let say  x/a=y/b=z/c = k

=> x = ak

   y = bk

   z = ck

xz+ac/xz-ac=yz+bc/yz-bc.

LHS

= (xz+ac)/(xz-ac)

= (ak.ck + ac) / (ak.ck - ac)

= ac(k² + 1) /ac(k² - 1)

= (k² + 1) /(k² - 1)

RHS

=(yz+bc)/(yz-bc0

= (bk.ck + bc) / (bk.ck - bc)

= bc(k² + 1) /bc(k² - 1)

=  (k² + 1) /(k² - 1)

(k² + 1) /(k² - 1)=  (k² + 1) /(k² - 1)

=> LHS = RHS

=> (xz+ac)/(xz-ac) = (yz+bc)/(yz-bc)

QED

Hence proved

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