Question

Упростите выражения(с
решением,как решали)
(1/a-b +1/b)×b/a
(1/y-1/x+y):x/y
(1/5c+1/10c)×c^2/6
(a-b/b-b-a/a)×b/a-b

Answer 1

$(\frac{1}{a-b} +\frac{1}{b} )*\frac{b}{a} =\frac{b+a-b}{b(a-b)} *\frac{b}{a} =\frac{1}{a-b} \\ \\ (\frac{1}{y} -\frac{1}{x+y} ):\frac{x}{y} =\frac{x+y-y}{y(x+y)} *\frac{y}{x} =\frac{1}{x+y} \\ \\ (\frac{1}{5c} +\frac{1}{10c} )*\frac{c^2}{6} =\frac{3}{10c}*\frac{c^2}{6} = \frac{c}{20}$

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