If x = 8ab/a+b, then find the value of x+4a/x-4a+ x+4b/x-4b is - Maths - Algebraic Expressions and Identities

Question

If x = 8ab/a+b, then find the value of x+4a/x-4a+ x+4b/x-4b
is

Ajanta Trivedi · Accepted Answer

given : x=8ab/a+b

the expression

$\frac{x + 4 a}{x - 4 a} = \frac{\frac{8 a b}{a + b} + 4 a}{\frac{8 a b}{a + b} - 4 a} = \frac{8 a b + 4 a (a + b)}{a + b} . \frac{a + b}{8 a b - 4 a (a + b)} = \frac{4 a^{2} + 12 a b}{- 4 a^{2} + 4 a b} = \frac{a + 3 b}{- a + b}$

similarly by symmetry:

$\frac{x + 4 b}{x - 4 b} = \frac{b + 3 a}{- b + a}$

now the expression is:

$\frac{x + 4 a}{x - 4 a} + \frac{x + 4 b}{x - 4 b} = \frac{a + 3 b}{- a + b} + \frac{3 a + b}{a - b} = \frac{- (a + 3 b) + 3 a + b}{a - b} = \frac{- a - 3 b + 3 a + b}{a - b} = \frac{2 a - 2 b}{a - b} = \frac{2 (a - b)}{a - b} = 2$

If x = 8ab/a+b, then find the value of x+4a/x-4a+ x+4b/x-4b is.