Question

If m= 4pq/3p+q then find the value of m+4p/m-p+m-3p/m-q

Answer 1

Answer:

m=4pq/3p+q

so m+4p=(4pq/(3p+q))+4p=(4pq+12p^2+4pq)/(3p+q)

so m+4p=(8pq+12p^2)/(3p+q)

m-p=(4pq/(3p+q))-p=(4pq-3p^2-pq)/(3p+q)

so m-p=(3pq-3p^2)/(3p+q)

m-3p=(4pq/(3p+q))-3p=(4pq-9p^2-3pq)/(3p+q)

so m-3p=(pq-9p^2)/(3p+q)

m-q=(4pq/(3p+q))-q=(4pq-3pq-q^2)/(3p+q)

so m-q=(pq-q^2)/(3p+q)

so (m+4p/m-p)+(m-3p/m-q)

= [{(8pq+12p^2)/(3p+q)}/{(3pq-3p^2)/(3p+q)}]+[{(pq-9p^2)/(3p+q)}/{(pq-q^2)/(3p+q)}]

= [(8pq+12p^2)/(3pq-3p^2)]+[(pq-9p^2)/(pq-q^2)]

=[(8q+12p)/{-3(p-q)}]+[(pq-9p^2)/{q (p-q)}]

=(8q^2+12pq-3pq+27p^2)/{-3q (p-q)}

=(8q^2+27p^2+9pq)/(-3q (p-q))