Question

упростите выражение (x+9/x-6):3x^2-18x+27/x^2-36
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Answer 1

$\tt\displaystyle (x+\frac{9}{x-6}):\frac{3x^2-18x+27}{x^2-36}=\frac{x+6}{3}$

$\tt\displaystyle 1)\ x+\frac{9}{x-6}=\frac{x(x-6)+9}{x-6}=\frac{x^2-6x+9}{x-6}\\\\\\2)\ \frac{x^2-6x+9}{x-6}:\frac{3x^2-18x+27}{x^2-36}=\frac{x^2-6x+9}{x-6}*\frac{x^2-36}{3x^2-18x+27}= \\\\\\=\frac{(x-3)^2*(x-6)(x+6)}{3(x-6)(x-3)^2}=\bold{\frac{x+6}{3}}$