Question

6.78 (1) можно пожалуйста письменно в виде фото​

Answer 1

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

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