Question

Упростить
a) a^2-b^2:5a^2*a:3a+3b
b)x+a:a:ax+x^2:a^2
v)a^-6:a^-3*a^-2

Answer 1

$a) : : frac{ {a}^{2} - {b}^{2} }{5 {a}^{2} } times frac{a}{3a + 3b} = frac{(a - b)(a + b)}{5a} times frac{1}{3(a + b)} = frac{a - b}{15a}$
$b) : : frac{x + a}{a} div frac{ax + {x}^{2} }{ {a}^{2} } = frac{x + a}{a} times frac{ {a}^{2} }{x(a + x)} = frac{a}{x}$
$v) : : {a}^{ - 6} div {a}^{ - 3} times {a}^{ - 2} = {a}^{ - 6 - (- 3)} times {a}^{ - 2} = {a }^{ - 3} times {a}^{ - 2} = {a}^{ - 3 - 2} = {a}^{ - 5}$