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

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