Question

(x+9 x-6) : 3x2-18x+27 x2-36

Answer 1

$(x + \frac{9}{x - 6} ) \div \frac{3 {x}^{2} - 18x + 27}{ {x}^{2} - 36} = \frac{x(x - 6) +9 }{x - 6} \div \frac{3( {x}^{2} - 6x + 9) }{(x - 6)(x + 6)} = \\ = \frac{ { {x}^{2} - 6x + 9} }{x - 6} \div \frac{3( {x}^{2} - 6x + 9) }{(x - 6)(x + 6)} = \frac{(x ^{2} - 6x + 9)(x - 6)(x + 6)}{(x - 6) \times 3( { {x}^{2} - 6x + 9)} } = \\ = \frac{x + 6}{3}$