Question

прошу упростить выражение ....
всего два задания на картинке во вложении

Answer 1

$1)\frac{a}{a-b}-\frac{a+b}{a}=\frac{a^{2}-(a-b)(a+b)}{a(a-b)}=\frac{a^{2}-a^{2}+b^{2}}{a(a-b)}=\frac{b^{2}}{a(a-b)}\\\\2)\frac{b^{2}}{a(a-b)}*\frac{a-b}{2b}=\frac{b}{2a}$

Answer 2

1)

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

2)

$\displaystyle \frac{ {b}^{2} }{a(a - b)} \times \frac{a - b}{2b} = \frac{ {b}^{2} \times (a - b)}{a(a - b) \times 2b} = \frac{ {b}^{2} }{2ab} = \boxed{ \frac{b}{2a} }$