Question

Пожалуйста помогите!!

Сократить пример (упростить) (b³/b²-8b+16 - b²/b-4) ÷ (b²/b²-16 - b/b-4)

Answer 1

$\displaystyle\bf\\\Big(\frac{b^{3} }{b^{2} -8b+16} -\frac{b^{2} }{b-4} \Big):\Big(\frac{b^{2} }{b^{2}-16 } -\frac{b}{b-4} \Big)=\\\\\\=\Big(\frac{b^{3} }{(b-4)^{2} } -\frac{b^{2} }{b-4} \Big):\Big(\frac{b^{2} }{(b-4)(b+4) } -\frac{b}{b-4} \Big)=\\\\\\=\frac{b^{3} -b^{2} \cdot(b-4)}{(b-4)^{2} } :\frac{b^{2} -b\cdot(b+4)}{(b-4)(b+4)} =\\\\\\=\frac{b^{3} -b^{3}+4b^{2} }{(b-4)^{2} } :\frac{b^{2} -b^{2} -4b}{(b-4)(b+4)} =\frac{ 4b^{2} }{(b-4)^{2} } :\frac{ -4b}{(b-4)(b+4)} =$

$\displaystyle\bf\\=-\frac{4b^{2} }{(b-4)^{2} } \cdot\frac{(b-4)(b+4)}{4b} =-\frac{b\cdot(b+4)}{b-4} =\frac{b^{2}+4b }{4-b}$