Question

(a /x+b) +(b /x+a) = a+b / x

Find the answer guys

Answer 1

Answer:

$\frac{a}{x + b} + \frac{b}{x + a} = \frac{a + b}{x} \\ \frac{a(x + a) + b(x + b)}{(x + a)(x + b)} = \frac{a + b}{x} \\ \frac{ax + {a}^{2} + bx + {b}^{2} }{ {x}^{2} + bx + ax + ab } = \frac{a + b}{x} \\ a {x}^{2} + {a}^{2} x + b {x}^{2} + {b}^{2} x = (a + b)( {x}^{2} + bx + ax + ab) \\ a {x }^{2} + {a}^{2}x + b {x}^{2} + {b}^{2}x = a {x}^{2} + abx + {a}^{2} x + {a}^{2} b + b {x}^{2} + {b}^{2} x + abx + a {b}^{2} \\ = abx + {a}^{2} b + abx + a {b}^{2} \\ = ab(x + a) \: \: \: \: + ab(x + b)$