Question

ЗРОБІТЬ 8 ТА 9 СРОЧНО!!ДАЮ 15 балів

Answer 1

Ответ:

Объяснение:

7.

$\displaystyle\\1)\\\\\frac{x+1}{x^2+x} *\frac{x^2-1}{2x^2+2x} =\frac{x+1}{x*(x+1)} *\frac{(x+1)*(x-1)}{2x*(x+1)}=\frac{1*(x-1)}{x*2x}=\frac{x-1}{2x^2} .\\\\2)\\\\\frac{x-1}{2x^2}:\frac{x^2-x}{2x^2} =\frac{x-1}{2x^2}*\frac{2x^2}{x*(x-1)}=\frac{1}{x} ..$

8.

$\displaystyle\\1)\\\\\frac{1+a}{1-a} +\frac{4a}{a^2-1}=\frac{a+1}{1-a}+ \frac{4a}{(a+1)*(a-1)} =\frac{a+1}{1-a}- \frac{4a}{(a+1)*(1-a)} \\\\\\=\frac{(a+1)*(a+1)-4a*1}{(a+1)*(1-a)}=\frac{(a+1)^2-4a}{(a+1)*(1-a)} =\frac{a^2+2a+1-4a}{(a+1)*(1-a)}=\\\\\\=\frac{a^2-2a-1}{(a+1)*(1-a)} =\frac{(a-1)^2}{(a+1)*(1-a)}= \frac{(1-a)^2}{(a+1)*(1-a)}=\frac{1-a}{a+1}.$

$2)\\\displaystyle\\ \frac{1-a}{a+1}:\frac{1-a}{a}= \frac{1-a}{a+1}*\frac{a}{1-a}=\frac{a}{a+1} .\\\\ 3)\\\\\frac{a}{a+1} +\frac{1}{a+1} =\frac{a+1}{a+1} =1.$

9.

$\displaystyle\\1)\\\\\frac{21+b}{b^2-8b+16} -\frac{b+3}{16-b^2} =\frac{b+21}{(b-4)^2} +\frac{b+3}{b^2-16} =\frac{b+21}{(b-4)^2}+\frac{b+3}{(b+4)*(b-4)} =\\\\\\=\frac{(b+21)*(b+4)+(b+3)*(b-4)}{(b-4)^2*(b+4)} =\frac{b^2+25b+84+b^2-b-12}{(b-4)^2*(b+4)} =\\\\\\=\frac{2b^2+24b+72}{(b-4)^2*(b+4)}=\frac{2*(b^2+12b+36)}{(b-4)^2*(b+4)} =\frac{2*(b+6)^2}{(b-4)^2*(b+4)}.$

$2)\\\displaystyle\\(\frac{b-4}{6+b} )^2*\frac{2*(b+6)^2}{(a-4)^2*(a+4)} =\frac{(b-4)^2}{(b+6)^2 } *\frac{2*(b+6)^2}{(b-4)^2*(b+4)} =\frac{2}{b+4} .\\\\3)\\\\\frac{14+3b}{4+b}-\frac{2}{b+4} =\frac{14+3b}{b+4}-\frac{2}{b+4} =\frac{14+3b-2}{b+4} =\frac{3b+12}{b+4} =\frac{3*(b+4)}{b+4}=3.$