Question

Calcule os quocientes:

a) a+ab/x² : 2+2b/3x

b) x²-4x/x²+1 : x²-16/2x²+2

c) x²+1/x²-2x+1 : x²+2x+1/x-1

Answer 1

a) $\frac{a(1+b)}{ x^{2} } . \frac{3x}{2(1+b)} = \frac{3a}{x}$

b)$\frac{ x(x -4)}{ (x^{2} +1)}. \frac{2( x^{2} +1)}{(x-4)(x+4)} = \frac{2x}{x+4}$

c)$\frac{ x^{2} +1}{(x-1)(x-1)} . \frac{x-1}{ x^{2} +2x+1} = \frac{ x^{2} +1}{(x-1)( x^{2} +2x+1)}$

$= \frac{ x^{2} +1}{ x^{3} +2 x^{2} +x- x^{2} -2x-1}$

$= \frac{ x^{2} +1}{ x^{3}+ x^{2} -x-1 }$