Question

Найдите значение выражения a/b если 7a+8b/9a-10b=9/11​

Answer 1

$\dfrac{7a+8b}{9a-10b}=\dfrac{9}{11}\\\\\\\dfrac{7a+8b}{9a-10b}=\dfrac{b\cdot (7\cdot \frac{a}{b}+8)}{b\cdot (9\cdot \frac{a}{b}-10)}=\dfrac{7\cdot \frac{a}{b}+8}{9\cdot \frac{a}{b}-10}=\dfrac{9}{11}\\\\\\11\cdot \Big(7\cdot \dfrac{a}{b}+8\Big)=9\cdot \Big(9\cdot \dfrac{a}{b}-10\Big)\\\\\\77\cdot \dfrac{a}{b}+88=81\cdot \dfrac{a}{b}-10\\\\\\4\cdot \dfrac{a}{b}=98\\\\\\\dfrac{a}{b}=24,5$