Question

if a+b/a-b and a cube-b cube/a cube +b cube are two rational expression then their product is

Answer 1

$\frac{(a + b)}{(a - b)} \times \frac{ {a}^{3} - {b}^{3} }{ {a}^{3} + {b}^{3} }$


as a^3 - b^3 = (a-b)(a^2+ab+b^2)
a^3 +b^3 = (a+b)(a^2-ab+b^2)

Use those two identities
and you'll get
$\frac{(a + b)}{(a - b)} \times \frac{ {a}^{3} - {b}^{3} }{ {a}^{3} + {b}^{3} } \\ \frac{(a + b)}{(a - b)} \times \frac{(a + b)( {a}^{2} + ab + {b}^{2}) }{(a - b)( {a}^{2} - ab + {b}^{2} )} \\ \\ = \frac{( {a}^{2} + ab + {b}^{2}) }{( {a}^{2} - ab + {b}^{2} )}$