If M = 4pq/3p+q then find the value of :
(M+4p)/(M-p) + (M-3p)/(M-q)
Answers
(M+4p)/(M-p) + (M-3p)/(M-q) = ( 4q² + 9pq + 27p²)/ (3q(q - p))
Step-by-step explanation:
M = 4pq/(3p + q)
M + 4p = 4pq/(3p + q) + 4p
=> M + 4p = (4pq + 12p² + 4pq) / (3p + q)
=> M + 4p = (8pq + 12p²) / (3p + q)
M - p = 4pq/(3p + q) - p
=> M - p = (4pq - 3p² - pq) / (3p + q)
=> M - p = (3pq - 3p²) / (3p + q)
(M + 4p)/(M - p) = (8pq + 12p²)/(3pq - 3p²) = 4(q + 3p)/3(q - p)
M - 3p = 4pq/(3p + q) - 3p
=> M - 3p = (4pq - 9p² - 3pq) / (3p + q)
=> M - 3p = (pq - 9p²) / (3p + q)
M - q = 4pq/(3p + q) - q
=> M - q = (4pq - 3pq - q²) / (3p + q)
=> M - q = (pq - q²) / (3p + q)
(M-3p)/(M-q) = (pq - 9p²) /(pq - q²) = p(q - 9p)/q(p - q) = p(9p - q)/q(q - p)
(M+4p)/(M-p) + (M-3p)/(M-q)
= 4(q + 3p)/3(q - p) + p(9p - q)/q(q - p)
= (1/3q(q - p)) ( 4q(q + 3p) + 3p(9p - q) )
= ( 4q² + 12pq + 27p² - 3pq) / (3q(q - p))
= ( 4q² + 9pq + 27p²)/ (3q(q - p))