Question

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нужно упростить примеры​

Answer 1

1)

$\frac{5m}{m - 3} - \frac{m + 12}{m - 3} = \frac{5m - m - 12}{m - 3} = \frac{4m - 12}{m - 3} = \frac{4(m - 3)}{m - 3} = 4$

2)

$\frac{a - x}{ {a}^{2} - 4} - \frac{x - 2}{4 - {a}^{2} } = \frac{a - x}{ {a}^{2} - 4 } - \frac{x - 2}{ - ( {a}^{2} - 4 )} = \frac{ a - x}{ {a}^{2} - 4 } + \frac{x - 2}{ {a}^{2} - 4 } = \frac{a - x + x - 2}{ {a}^{2} - 4 } = \frac{a - 2}{(a - 2)(a + 2)} = \frac{1}{a + 2}$

3)

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

4)

$\frac{3a}{a - 3} + a = \frac{3a}{a - 3} + \frac{a(a - 3)}{a - 3} = \frac{3a}{a - 3} + \frac{ {a}^{2} - 3a }{a - 3} = \frac{3a + {a}^{2} - 3a }{a - 3} = \frac{ {a}^{2} }{a - 3}$