Question

допустимо: (3a -5b)÷(a +3b)= a+3b не равно нулю

Answer 1

$\frac{3a - 5b}{a + 3b} = a + 3b \\ \\ \frac{3a - 5b}{a + 3b} - a - 3b = 0 \\ \\ \frac{3a - 5b}{a + 3b} - \frac{a {}^{2} - 9b {}^{2} }{a + 3b} = 0 \\ \\ \frac{3a - 5b - a {}^{2} - 9b {}^{2} }{a + 3b} = 0 \\ \\ \frac{3a - 5b - (a - 3b)(a + 3b)}{a + 3b} = 0 \\ \\ 3a - 5b - a + 3b = 0 \\ \\ 2a - 2b = 0 \\ \\ 2(a - b) = 0 \\ \\ 2a = 2b \\ \\ a = b$
a=b, b € R