Question

Довести тотожність: дам 100 балов

Answer 1

$\displaystyle\bf\\\Big(c-\frac{12c-4}{c+8} \Big):\Big(4c-\frac{40c}{c+8} \Big)=\\\\\\=\frac{c^{2} +8c-12c+4}{c+8} :\frac{4c^{2}+32c-40c }{c+8} =\\\\\\=\frac{c^{2} -4c+4}{c+8} :\frac{4c^{2} -8c}{c+8} =\frac{(c-2)^{2} }{c+8} :\frac{4c\cdot(c -2)}{c+8} =\\\\\\=\frac{(c-2)^{2} }{c+8} \cdot\frac{c+8}{4c\cdot(c-2) } =\frac{c-2}{4c} \\\\\\\frac{c-2}{4c} =\frac{c-2}{4c}$