Question

if a/b = c/d, show that a3 c + ac3 / b3d +bd3 = (a+c)4 / (b+d)4

Answer 1

Let
$\frac{a}{b} = \frac{c} {d} = k$

$a = bk$

$c = dk$

$\frac{ {(a + c)}^{4} }{ {(b + d)}^{4} } = \frac{ {(bk + dk)}^{4} }{ {(b + d)} ^{4}} = {k}^{4}$

$\frac{ {a}^{3} c + a {c}^{3} }{ {b}^{3}d + b {d}^{3} } = \frac{ {b}^{3} d {k}^{4} + b {d}^{3} {k}^{4} }{ {b}^{3}d + b {d}^{3}} = {k}^{4} = \frac{ {(a + c)}^{4} }{ {(b + d)}^{4} }$

Hence , proved.