Question

Упростите сумму или разность

Answer 1

$...=\frac{a^2 +b^2+ 2ab}{2a \cdot (a + b)}=\frac{(a+b)^2}{2a \cdot (a+b)}=\frac{a+b}{2a} \\ \\ ...= \frac{4y-2\cdot (y+x)}{(y-x)\cdot (y+x)}=\frac{4y -2y -2x}{(y-x) \cdot (y+x)} = \frac{2 \cdot (y-x)}{(y-x) \cdot (y+x)}=\frac{2}{y+x} \\ \\ ...=\frac{6a-3\cdot (a+b)}{(a-b) \cdot (a+b)}=\frac{3 \cdot (a -b)}{(a-b) \cdot (a+b)}=\frac{3}{a+b}$

Answer 2

$66) \frac{a ^{2} +b ^{2} }{2a ^{2} +2ab} + \frac{b}{a+b} = \frac{a ^{2} +b ^{2} }{2a(a+b)} + \frac{b}{a+b} = \frac{a ^{2} +b ^{2} }{2a(a+b)} + \frac{2ab}{2a(a+b)} = \\ \\ = \frac{a ^{2} +b ^{2} +2ab}{2a(a+b)} = \frac{(a+b) ^{2} }{2a(a+b)} = \frac{a+b}{2a}$

$67) \frac{4y}{y ^{2}- x^{2} } - \frac{2}{y-x} = \frac{4y}{(y-x)(y+x)} - \frac{2}{y-x} = \frac{4y}{(y-x)(y+x)} - \\ \\ -\frac{2(y+x)}{(y-x)(y+x)} = \frac{4y-2y-2x}{(y-x)(y+x)} = \frac{2y-2x}{(y-x)(y+x)} = \frac{2(y-x)}{(y-x)(y+x)} =\\ \\ = \frac{2}{y+x}$

$68) \frac{6a}{a ^{2} -b ^{2} } - \frac{3}{a-b} = \frac{6a}{(a-b)(a+b)} - \frac{3(a+b)}{(a-b)(a+b)} = \frac{6a-3a-3b}{(a-b)(a+b)} = \\ \\ = \frac{3a-3b}{(a-b)(a+b)} = \frac{3(a-b)}{(a-b)(a+b)} = \frac{3}{a+b}$