if m= 4pq/p+q then find the value of (m+2p/m-2p)+(m+2q/m-2q) - Maths - Algebraic Expressions

Question

if m= 4pq/p+q then find the value of (m+2p/m-2p)+(m+2q/m-2q)

Manbar Singh · Accepted Answer

We have,     m = 4pqp+q⇒m = 2p 
 2qp+q⇒m2p = 2qp+q⇒m+2pm-2p = 2q+p+q2q-p-q   Componendo and dividendo⇒m+2pm-2p = 3q+pq-p    
1Again,  m = 4pqp+q⇒m = 2p 
 2qp+q⇒m2q = 2pp+q⇒m+2qm-2q = 2p+p+q2p-p-q   Componendo and dividendo⇒m+2qm-2q = 3p+qp-q    
2adding 1 and 2, we get     m+2pm-2p + m+2qm-2q = 3q+pq-p + 3p+qp-q ⇒m+2pm-2p + m+2qm-2q= 3q+pq-p - 3p+qq-p ⇒m+2pm-2p + m+2qm-2q= 3q+p-3p-qq-p = 2q-pq-p = 2