Question

. (2 бали) Спростіть вираз по фото​

Answer 1

$\displaystyle\bf\\\frac{m+3}{5m-10} -\frac{m-3}{5m+10}+\frac{4}{4-m^{2} } = \frac{m+3}{5\cdot(m-2)} -\frac{m-3}{5\cdot(m+2)}-\frac{4}{(m-2)(m+2)} = \\\\\\=\frac{(m+3)(m+2)-(m-3)(m-2)-4\cdot 5}{5(m-2)(m+2)} =\\\\\\=\frac{m^{2} +2m+3m+6-m^{2} +2m+3m-6-20}{5(m-2)(m+2)} =\frac{10m-20}{5(m-2)(m+2)}=\\\\\\=\frac{10\cdot(m-2)}{5(m-2)(m+2)} =\frac{2}{m+2} \\\\\\m=-\frac{1}{3} \\\\\\\frac{2}{m+2} =\frac{2}{-\dfrac{1}{3} +2} =\frac{2}{\frac{5}{3} } =\frac{2\cdot 3}{5} =\frac{6}{5} =1,2$