Question

(10a2)(a3+b3)/(6a4-6a3b+6a2b2)

Answer 1

▪A tomar en cuenta

° Factor Común:
$\boxed{ab + ac = a(b + c)}$

° Suma de Cubos Perfectos:
$\boxed{ {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )}$


▪Enunciado
$\boxed{ \frac{(10 {a}^{2})( {a}^{3} + {b}^{3} )}{(6 {a}^{4} - 6 {a}^{3} b + 6 {a}^{2} {b}^{2} )} }$

▪Procedimiento

$\frac{(10 {a}^{2})( {a}^{3} + {b}^{3} )}{(6 {a}^{4} - 6 {a}^{3} b + 6 {a}^{2} {b}^{2} )} = \\ \\ \frac{(10 {a}^{2})( {a}^{3} + {b}^{3}) }{6 {a}^{2} ( {a}^{2} - ab + {b}^{2} )} = \\ \\ \frac{(10 {a}^{2} )(a + b) ( {a}^{2} - ab + {b}^{2}) }{6 {a}^{2} ( {a}^{2} - ab + {b}^{2} )} = \\ \\ \frac{10 {a}^{2}(a + b) }{6 {a}^{2} } = \\ \\ \boxed{ \boxed{\frac{5(a + b)}{3} }}$