Question

Нужно упростить выражения! 5 и 7! Даю 40 баллов!!

Answer 1

5)

$\displaystyle\bf\\1)\\\\\frac{a-b}{a^{2}+ab } -\frac{a}{ab+b^{2} }=\frac{a-b}{a\cdot(a+b)} -\frac{a}{b\cdot(a+b)} =\\\\\\=\frac{(a-b)\cdot b-a\cdot a}{ab\cdot(a+b)} =\frac{ab-b^{2} - a^{2} }{ab(a+b)} =-\frac{a^{2} -ab+b^{2} }{ab(a+b)} \\\\\\2)\\\\\frac{b^{2} }{a^{3} -a b^{2} } +\frac{1}{a+b}=\frac{b^{2} }{a\cdot(a^{2} - b^{2}) } +\frac{1}{a+b}=\\\\\\=\frac{b^{2} }{a\cdot(a- b)(a+b) } +\frac{1}{a+b}=\frac{b^{2}+a\cdot(a-b) }{a(a-b)(a+b)} =$

$\displaystyle\bf\\=\frac{b^{2}+a^{2} -ab}{a(a-b)(a+b)} =\frac{a^{2} -ab+b^{2} }{a(a-b)(a+b)} \\\\\\3)\\\\-\frac{a^{2} -ab+b^{2} }{ab(a+b)} :\frac{a^{2} -ab+b^{2} }{a(a-b)(a+b)} =\\\\\\=-\frac{a^{2} -ab+b^{2} }{ab(a+b)} \cdot\frac{a(a-b)(a+b)}{a^{2}-ab+b^{2} } =-\frac{a-b}{b}=\frac{b-a}{b}$

7)

$\displaystyle\bf\\1)\\\\\frac{a-3}{a^{2}-3a+9 } +\frac{a+9}{a^{3}+27 } =\frac{a-3}{a^{2}-3a+9 } +\frac{a+9}{(a+3)(a^{2} -3a+9) } =\\\\\\=\frac{(a-3)\cdot(a+3)+a+9}{(a+3)(a^{2}-3a+9) } =\frac{a^{2}-9 +a+9}{(a+3)(a^{2}-3a+9) } =\\\\\\=\frac{a^{2} +a}{(a+3)(a^{2}-3a+9) } \\\\\\2)\\\\\\\frac{a^{3} +27}{a-1} \cdot \frac{a^{2} +a}{(a+3)(a^{2}-3a+9) } :\frac{a^{2} +a}{a^{2}-1 } =\\\\\\=\frac{(a+3)(a^{2} -3a+9)}{a-1} \cdot \frac{a^{2} +a}{(a+3)(a^{2}-3a+9) } \cdot\frac{(a-1)(a+1)}{a^{2} +a} =a+1$