Question

Спростіть вираз, допоможіть будь ласка, даю 60 балів

Answer 1

$= \frac{ { (2a + 1) }^{2} - {(2a - 1)}^{2} }{(2a - 1)(2a + 1)} +\\+ \frac{2a}{3(2a + 1)} = \\ = \frac{(2a + 1 + 2a - 1)(2a + 1 - 2a + 1)}{(2a - 1)(2a + 1)} + \\ + \frac{2a}{3(2a + 1)} = \\= \frac{4a \times 2}{ \:(2a - 1)(2a + 1)} + \frac{2a}{3(2a + 1)} = \\ = \frac{2a(4 \times 3 + 2a - 1)}{3(4 {a}^{2} - 1)} = \frac{2a(2a + 11) }{3(4{a}^{2} - 1) } = \\ = \frac{4 {a}^{2} + 22a}{12 {a}^{2} - 3}$

Answer 2

$\displaystyle \left( \frac{2a+1}{2a-1} -\frac{2a-1}{2a+1} \right) +\frac{2a}{6a+3} = \frac{(2a+1)^2-(2a-1)^2}{(2a-1)(2a+1)} \right) +\frac{2a}{3(2a+1)}= \\\\\\ = \frac{(2a+1-2a+1)(2a+1+2a-1)}{(2a-1)(2a+1)} \right) +\frac{2a}{3(2a+1)}= \\\\\\= \frac{2 \cdot4a}{(2a-1)(2a+1)} \right) +\frac{2a}{3(2a+1)}= \frac{3 \cdot8a+2a(2a-1)}{3(2a-1)(2a+1)}= \\\\\\ =\frac{24a+4a^2-2a}{3(4a^2-1)}= \frac{4a^2+22a}{12a^2-3}$