Question

а+1
a
+
при а= 0,5.
а
а — 1

Answer 1

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

а = 0.5,

$\frac{2 {a}^{2} - 1}{ {a}^{2} - a } = \frac{2 \times {(0.5)}^{2} - 1}{ {(0.5)}^{2} - 0.5 } = \frac{2 \times 0.25 - 1}{0.25 - 0.5} = \frac{0.5 - 1}{ - 0.25} = \frac{ - 0.5}{ - 0.25} = \frac{0.5}{0.25} = \frac{ \frac{5}{10} }{ \frac{25}{100} } = \frac{5}{10} \times \frac{100}{25} = 2$

Ответ: 2