Question

Найдите (a+9b+16) / (a+3b+8), если a/b=3

Answer 1

$frac{a}{b}=3\\ frac{a+9b+16}{a+3b+8}= frac{ frac{a}{b}+ frac{9b}{b}+ frac{16}{b} }{ frac{a}{b}+ frac{3b}{b}+ frac{8}{b} }= frac{ frac{a}{b}+9+ frac{16}{b} }{ frac{a}{b}+3+ frac{8}{b} }= frac{3+9+ frac{16}{b} }{3+3+ frac{8}{b} }= frac{12+frac{16}{b}}{6+frac{8}{b}}=\\= frac{ frac{12b+16}{b} }{ frac{6b+8}{b} }= frac{12b+16}{6b+8}= frac{4(3b+4)}{2(3b+4)}=2$