Tính:a) \(\dfrac{{3{a^2}}}{{10{b^3}}} \cdot \dfrac{{15b}}{{9{a^4}}}\) b) \(\dfrac{{x - 3}}{{{x^2}}} \cdot \dfrac{{4x}}{{{x^2} - 9}}\)c) \(\dfrac{{{a^2} - 6a + 9}}{{{a^2} + 3a}} \cdot \dfrac{{2a + 6}}{{a - 3}}\) d) \(\dfrac{{x + 1}}{x} \cdot \left( {x + \dfrac{{2 - {x^2}}}{{{x^2} - 1}}}...
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Tính:
a) \(\dfrac{{3{a^2}}}{{10{b^3}}} \cdot \dfrac{{15b}}{{9{a^4}}}\) b) \(\dfrac{{x - 3}}{{{x^2}}} \cdot \dfrac{{4x}}{{{x^2} - 9}}\)
c) \(\dfrac{{{a^2} - 6a + 9}}{{{a^2} + 3a}} \cdot \dfrac{{2a + 6}}{{a - 3}}\) d) \(\dfrac{{x + 1}}{x} \cdot \left( {x + \dfrac{{2 - {x^2}}}{{{x^2} - 1}}} \right)\)
a) \(\dfrac{3a^2}{10b^3}\cdot\dfrac{15b}{9a^4}\)
\(=\dfrac{3a^2\cdot15b}{10b^3\cdot9a^4}\)
\(=\dfrac{1\cdot3}{2\cdot b^2\cdot3\cdot a^2}=\dfrac{3}{6a^2b^2}\)
b) \(\dfrac{x-3}{x^2}\cdot\dfrac{4x}{x^2-9}\)
\(=\dfrac{x-3}{x^2}\cdot\dfrac{4x}{\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{\left(x-3\right)\cdot4x}{x^2\left(x+3\right)\left(x-3\right)}\)
\(=\dfrac{4}{x\left(x+3\right)}\)
c) \(\dfrac{a^2-6x+9}{a^2+3a}\cdot\dfrac{2a+6}{a-3}\)
\(=\dfrac{\left(a-3\right)^2}{a\left(a+3\right)}\cdot\dfrac{2\cdot\left(a+3\right)}{a-3}\)
\(=\dfrac{\left(a-3\right)^2\cdot2\cdot\left(a+3\right)}{a\left(a+3\right)\left(a-3\right)}\)
\(=\dfrac{2\left(a-3\right)}{a}\)
d) \(\dfrac{x+1}{x}\cdot\left(x+\dfrac{2-x^2}{x^2-1}\right)\)
\(=\dfrac{\left(x+1\right)\cdot x}{x}+\dfrac{x+1}{x}\cdot\dfrac{2-x^2}{x^2-1}\)
\(=x+1+\dfrac{x+1}{x}\cdot\dfrac{2-x^2}{\left(x+1\right)\left(x-1\right)}\)
\(=x+\dfrac{2-x^2}{x\left(x-1\right)}\)
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