Question

Me ajudem com esse cálculo de louco

Answer 1

Bom dia

$M=a+ \frac{b-a}{1+ab} = \frac{a*(1+ab)+(b-a)}{1+ab} = \frac{a+ a^{2}b+b-a }{1+ab} = \frac{b+ a^{2}b }{1+ab} = \frac{b(1+ a^{2} )}{1+ab}$

$N=1- \frac{ab+ b^{2} }{1+ab}= \frac{(1+ab)-(ab+ b^{2} )}{1+ab} = \frac{1+ab-ab- b^{2} }{1+ab} = \frac{1- b^{2} }{1+ab}$

$\frac{M}{N} = \frac{ \frac{b(1+ a^{2} )}{1+ab} }{ \frac{1- b^{2} }{1+ab} } = \frac{b(1+ a^{2} )}{1- b^{2} }$