Thực hiện phép tính: a) 24y^5/7x^2.( - 49x/12y^3); b) - 36y^3/15x^4.( -45x^2/9y^3); c) x^2 - y^2/x^2.x^4/( x + y)^2; d) x + 3/x^2 - 1.1 - 3x + 3x^2 - x^3/9x + 27

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Thực hiện phép tính:

a) \(\frac{{24{y^5}}}{{7{x^2}}}.\left( { - \frac{{49x}}{{12{y^3}}}} \right)\);

b) \( - \frac{{36{y^3}}}{{15{x^4}}}.\left( { - \frac{{45{x^2}}}{{9{y^3}}}} \right)\);

c) \(\frac{{{x^2} - {y^2}}}{{{x^2}}}.\frac{{{x^4}}}{{{{\left( {x + y} \right)}^2}}}\);

d) \(\frac{{x + 3}}{{{x^2} - 1}}.\frac{{1 - 3x + 3{x^2} - {x^3}}}{{9x + 27}}\).

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Giải thích

Lời giải

a) \(\frac{{24{y^5}}}{{7{x^2}}}.\left( { - \frac{{49x}}{{12{y^3}}}} \right) = - \frac{{24{y^5}.49x}}{{7{x^2}.12{y^3}}} = - \frac{{14{y^2}}}{x}\).

b) \( - \frac{{36{y^3}}}{{15{x^4}}}.\left( { - \frac{{45{x^2}}}{{9{y^3}}}} \right) = \frac{{36{y^3}.45{x^2}}}{{15{x^4}.9{y^3}}} = \frac{{12}}{{{x^2}}}\).

c) \(\frac{{{x^2} - {y^2}}}{{{x^2}}}.\frac{{{x^4}}}{{{{\left( {x + y} \right)}^2}}} = \frac{{\left( {{x^2} - {y^2}} \right).{x^4}}}{{{x^2}.{{\left( {x + y} \right)}^2}}}\)

\( = \frac{{\left( {x - y} \right)\left( {x + y} \right).{x^4}}}{{{x^2}.{{\left( {x + y} \right)}^2}}} = \frac{{{x^2}\left( {x - y} \right)}}{{x + y}}\).

d) \(\frac{{x + 3}}{{{x^2} - 1}}.\frac{{1 - 3x + 3{x^2} - {x^3}}}{{9x + 27}}\)

\( = \frac{{\left( {x + 3} \right)\left( {1 - 3x + 3{x^2} - {x^3}} \right)}}{{\left( {{x^2} - 1} \right)\left( {9x + 27} \right)}}\)

\( = \frac{{\left( {x + 3} \right){{\left( {1 - x} \right)}^3}}}{{\left( {x - 1} \right)\left( {x + 1} \right).9.\left( {x + 3} \right)}}\)

\( = - \frac{{\left( {x + 3} \right){{\left( {x - 1} \right)}^3}}}{{\left( {x - 1} \right)\left( {x + 1} \right).9.\left( {x + 3} \right)}}\)

\( = - \frac{{{{(x - 1)}^2}}}{{9\left( {x + 1} \right)}}\).