Question

доведіть тотожність ​

Answer 1

$\displaystyle\bf\\1)\\\\\frac{6b}{2b+5} -\frac{16b}{4b^{2} +20b+25} =\frac{6b}{2b+5}-\frac{16b}{(2b+5)^{2} } =\\\\\\=\frac{6b\cdot(2b+5)-16b}{(2b+5)^{2} }=\frac{12b^{2} +30b-16b}{(2b+5)^{2} } =\\\\\\=\frac{12b^{2}+14b }{(2b+5)^{2} }=\frac{2b\cdot(6b+7)}{(2b+5)^{2} } \\\\\\2)\\\\\frac{2b\cdot(6b+7)}{(2b+5)^{2} } :\frac{6b+7}{4b^{2} -25} =\frac{2b\cdot(6b+7)}{(2b+5)^{2} }\cdot\frac{4b^{2} -25}{6b+7} =$

$\displaystyle\bf\\=\frac{2b\cdot(6b+7)}{(2b+5)^{2} } \cdot\frac{(2b+5)(2b-5)}{6b+7} =\frac{2b\cdot(2b-5)}{2b+5} =\frac{4b^{2} -10b}{2b+5} \\\\\\3)\\\\\frac{4b^{2} -10b}{2b+5} +\frac{10b-25}{2b+5} =\frac{4b^{2} -10b+10b-25}{2b+5} =\frac{4b^{2} -25}{2b+5} =\\\\\\=\frac{(2b-5)(2b+5)}{2b+5} =2b-5\\\\\\2b-5=2b-5$

Что и требовалось доказать