Thực hiện phép tính ((3x / (1 - 3x) + 2x / (3x + 1)) : (6x^2 + 10x) / (1 - 6x + 9x^2)
Thực hiện phép tính:
\(\left( {\frac{{3x}}{{1 - 3x}} + \frac{{2x}}{{3x + 1}}} \right):\frac{{6{x^2} + 10x}}{{1 - 6x + 9{x^2}}}\).
\(\left( {\frac{{3x}}{{1 - 3x}} + \frac{{2x}}{{3x + 1}}} \right):\frac{{6{x^2} + 10x}}{{1 - 6x + 9{x^2}}}\)
\( = \left[ {\frac{{3x\left( {3x + 1} \right)}}{{\left( {1 - 3x} \right)\left( {3x + 1} \right)}} + \frac{{2x\left( {1 - 3x} \right)}}{{\left( {1 - 3x} \right)\left( {3x + 1} \right)}}} \right]:\frac{{2x\left( {3x + 5} \right)}}{{{{\left( {1 - 3x} \right)}^2}}}\)
\( = \left[ {\frac{{3x\left( {3x + 1} \right) + 2x\left( {1 - 3x} \right)}}{{\left( {1 - 3x} \right)\left( {3x + 1} \right)}}} \right]:\frac{{2x\left( {3x + 5} \right)}}{{{{\left( {1 - 3x} \right)}^2}}}\)
\( = \left[ {\frac{{9{x^2} + 3x + 2x - 6{x^2}}}{{\left( {1 - 3x} \right)\left( {3x + 1} \right)}}} \right]:\frac{{2x\left( {3x + 5} \right)}}{{{{\left( {1 - 3x} \right)}^2}}}\)
\( = \left[ {\frac{{3{x^2} + 5x}}{{\left( {1 - 3x} \right)\left( {3x + 1} \right)}}} \right]:\frac{{2x\left( {3x + 5} \right)}}{{{{\left( {1 - 3x} \right)}^2}}}\)
\( = \frac{{x\left( {3x + 5} \right)}}{{\left( {1 - 3x} \right)\left( {3x + 1} \right)}}:\frac{{2x\left( {3x + 5} \right)}}{{{{\left( {1 - 3x} \right)}^2}}}\)
\( = \frac{{x\left( {3x + 5} \right)}}{{\left( {1 - 3x} \right)\left( {3x + 1} \right)}}.\frac{{{{\left( {1 - 3x} \right)}^2}}}{{2x\left( {3x + 5} \right)}}\)
\( = \frac{{1 - 3x}}{{2\left( {3x + 1} \right)}}\).