Question

Срочно, 98 баллов помогите крч по алгебре

Answer 1

$1) \frac{ {m}^{2} - {n}^{2} }{m - n} \\ \\ \frac{ {2.5}^{2} - ({ - 7.5)}^{2} }{2.5 - ( - 7.5)} = \frac{ \frac{25}{4} - ( - \frac{ {15}^{2} }{4} ) }{10} = \frac{25 - {15}^{2} }{4} = - 5$

$2) \frac{1}{4x} - \frac{4x + y}{4xy} = \frac{y - (4x + y)}{4xy} = \\ \\ = - \frac{4x}{4xy} = - \frac{1}{y} \\ \\ - \frac{1}{ \frac{1}{2} } = - 2$

$3)(x - 3) \div \frac{ {x}^{2} - 6x + 9}{x + 3} = (x - 3) \times \frac{x + 3}{ {x}^{2} - 6x + 9 } = \\ \\ = \frac{(x - 3)(x + 3)}{(x - 3)^{2} } = \frac{x + 3}{x - 3}$

$4)16 \times {2}^{ - 5} \times {2}^{6} = {2}^{4} \times {2}^{ - 5} \times {2}^{6} = \\ = {2}^{4 - 5 + 6} = {2}^{5} = 32$

$5)3 \sqrt{2} + \sqrt{50} - 2 \sqrt{8} = 3 \sqrt{2} + 5 \sqrt{2} - 4 \sqrt{2} = 4 \sqrt{2}$

$6) \frac{49 - {a}^{2} }{a - 9} ( \frac{a}{a - 7} - \frac{2a}{ {a}^{2} - 14a + 49} ) + \frac{14a}{a - 7} = \\ \\ = \frac{(7 - a)(7 + a)}{a - 9} - \frac{a \times (a - 7) - 2a}{ {(a - 7)}^{2} } + \frac{14a}{a - 7} = \\ \\ = \frac{ - (7 + a)}{a - 9} - \frac{ {a}^{2} - 9a }{a - 7} + \frac{14a}{a - 7} = \\ \\ = - \frac{7a + {a}^{2} }{a - 7} + \frac{14a}{a - 7} = \\ \\ = \frac{ - 7a - {a}^{2} + 14a }{a - 7} = \frac{7a - {a}^{2} }{a - 7} = \frac{ - (a - 7) \times a}{a - 7} = \\ \\ = - a$