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a) \(\frac{30x^3}{11y^2}.\frac{121y^5}{25x}=\frac{6x^2.11y^3}{5}=\frac{66x^2y^3}{5}\)
b) \(\frac{x+3}{x^2-4}.\frac{8-12x+6x^2-x^3}{9x+27}=\frac{x+3}{\left(x-2\right)\left(x+2\right)}.\frac{\left(2-x\right)^3}{9\left(x+3\right)}\)
\(=\frac{-\left(x-2\right)^2}{9\left(x+2\right)}\)
p/s: chúc bạn học tốt
\(\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x-6}{4-9x^2}\)
\(=\frac{3x+2}{9x^2-4}-\frac{3x-2}{9x^2-4}+\frac{3x-6}{9x^2-4}\)
\(=\frac{3x+2-3x+2+3x-6}{9x^2-4}\)
\(=\frac{3x-2}{9x^2-4}\)
\(=\frac{1}{3x+2}\)
\(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x^2}{x^2-9}\)
\(=\frac{18}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\) \(-\frac{3\left(x+3\right)}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\)\(-\frac{x^2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x-3\right)}\)
\(=\frac{18-3x-9-x^3+3x^2}{\left(x-3\right)^2\left(x+3\right)}\)
\(=\frac{-x^3+3x^2-3x+9}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{\left(-x^2-3\right)\left(x-3\right)}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{-x^2-3}{\left(x-3\right)\left(x+3\right)}\)
học tốt
a) \(\frac{9x^2}{11y^2}:\frac{6x}{11y}=\frac{9x^2}{11y^2}\cdot\frac{11y}{6x}=\frac{3xy}{2}\)
b) \(\frac{x^2-49}{x-7}+x-2=\frac{\left(x-7\right)\left(x+7\right)}{x-7}+x-2=x+7+x-2=2x+5\)
c) \(\frac{3}{x+3}+\frac{1}{x-3}-\frac{18}{9-x^2}\)
= \(\frac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+\frac{1\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{18}{\left(3-x\right)\left(x+3\right)}\)
= \(\frac{3x-9}{\left(x-3\right)\left(x+3\right)}+\frac{x+3}{\left(x-3\right)\left(x+3\right)}+\frac{18}{\left(x-3\right)\left(x+3\right)}\)
= \(\frac{3x-9+x+3+18}{\left(x-3\right)\left(x+3\right)}\)
= \(\frac{4x+12}{\left(x-3\right)\left(x+3\right)}\)
= \(\frac{4\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\frac{4}{x-3}\)(đk: \(x-3\ne0\)=> \(x\ne3\))