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)

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