Question

Упростите выражение

Answer 1

Ответ:

$\frac{15y + 6}{y - 10} - \frac{y - 9}{y - 10} + \frac{6y + 9}{10 - y} = \frac{15y + 6 - y + 9}{y - 10} + \frac{6y + 9}{10 - y} = \frac{14y + 15}{y - 10} + \frac{6y + 9}{10 - y } = \frac{(14y + 15)(10 - y) + (6y + 9)(y - 10)}{(y - 10)(10 - y)} = \frac{140y - 14 {y}^{2} + 150 - 15y + 6 {y}^{2} - 60y + 9y - 90 }{10y - {y}^{2} - 100 + 10y } = \frac{ - 8 {y}^{2} + 74y + 60 }{ - {y}^{2} + 20y - 100 } = \frac{4 {y}^{2} - 37 - 30}{ {y}^{2} - 20y + 100 } = \frac{4(y - 10)(y + 0.75)}{(y - 10)^{2} } = \frac{4(y + 0.75)}{y - 10} = \frac{4y + 3}{y - 10}$