PHẦN II. TỰ LUẬN

Thực hiện phép tính:

a) \[\left( {x + \;5} \right)\left( {3x + \;2y} \right).\] 

b) \[{\left( {3x - \;2} \right)^2}\; - \;\left( {x + \;3} \right)\left( {x - \;3} \right).\]  

c) \[\frac{5}{{x + 1}}\; - \frac{2}{{x - 1}}\; + \frac{{4x}}{{{x^2} - 1}}.\]

a) \[\left( {x + \;5} \right)\left( {3x + \;2y} \right)\]

\[ = 3{x^2} + 2xy + 15x + 10y.\]

b) \[{\left( {3x - \;2} \right)^2}\; - \;\left( {x + \;3} \right)\left( {x - \;3} \right)\]

\[ = 9{x^2} - 12x + 4 - \left( {{x^2} - 9} \right)\]

\[ = 9{x^2} - 12x + 4 - {x^2} + 9\]

\[ = 8{x^2} - 12x + 13\]

c) \[\frac{5}{{x + 1}}\; - \frac{2}{{x - 1}}\; + \frac{{4x}}{{{x^2} - 1}}\]

\[ = \frac{{\;5\;}}{{x + \;1}} - \frac{2}{{x - 1}} + \frac{{4x}}{{\left( {x\; + \;1} \right)\left( {x\; - 1} \right)}}\]

\[ = \frac{{\;5\left( {x\; - 1} \right) - 2\left( {x\; + \;1} \right) + 4x\;}}{{\left( {x\; + \;1} \right)\left( {x\; - 1} \right)}}\]

\[ = \frac{{\;5x - 5 - 2x - 2 + 4x\;}}{{\left( {x\; + \;1} \right)\left( {x\; - 1} \right)}}\]

\[ = \frac{{\;7\left( {x\; - 1} \right)\;}}{{\left( {x\; + \;1} \right)\left( {x\; - 1} \right)}} = \frac{{\;7\;}}{{x\; + \;1}}.\]