Question

Вычислить, НЕ ПРИЛОЖЕНИЯМИ!!

Answer 1

а) (4-9х)/9х³-(5х-6)/6х²=(8-18х-15х²+18х)/18х³=(8-15х²)/18х³

б) 6/х-42/(х²+7х)=(6х+42-42)/(х*(х+7))=6/(х+7)

в) х/(4+х)-х²/(х-4)(х+4)=(х²-4х-х²)/(х²-16)=-4х/(х²-16)

г)(18а²-3а-18а²)/(1+6а))=-3а/(1+6а)

Answer 2

$1)\frac{4-9x}{9x^{3}}-\frac{5x-6}{6x^{2}}=\frac{(4-9x)*2-(5x-6)*3x}{18x^{3}}=\frac{8-18x-15x^{2}+18x }{18x^{3}}= \frac{-15x^{2}+8 }{18x^{3}}=-\frac{15x^{2}-8}{18x^{3} }$

$2)\frac{6}{x}-\frac{42}{x^{2}+7x }=\frac{6}{x}-\frac{42}{x(x+7)}=\frac{6*(x+7)-42}{x(x+7)}=\frac{6x+42-42}{x(x+7)}=\frac{6x}{x(x+7)}=\frac{6}{x+7}$

$3)\frac{x}{4+x}-\frac{x^{2}}{x^{2}-16}=\frac{x}{x+4}-\frac{x^{2}}{(x+4)(x-4)}=\frac{x*(x-4)-x^{2}}{(x+4)(x-4)}=\frac{x^{2}-4x-x^{2}}{x^{2}-16}=\frac{-4x}{x^{2}-16}=\frac{4x}{16-x^{2}}$

$4)\frac{18a^{2} }{1+6a}-3a=\frac{18a^{2}-3a*(1+6a)}{1+6a}=\frac{18a^{2}-3a-18a^{2}}{1+6a}=\frac{-3a}{1+6a}=-\frac{3a}{1+6a}$