Thực hiện phép tính:a ) 5y − 4x − 8 − ( y + 2x − 3 ) . b) ( 2x − y ) ( 4x − 3y ) − 20x^3y^2 : ( − 2x^2y ) .

Hướng dẫn giải:

a) \(5y - 4x - 8 - \left( {y + 2x - 3} \right)\) \( = 5y - 4x - 8 - y - 2x + 3\) \( = \left( { - 2x - 4x} \right) + \left( {5y - y} \right) + \left( {3 - 8} \right)\) \( = - 6x + 4y - 5\).

b) \(\left( {2x - y} \right)\left( {4x - 3y} \right) - 20{x^3}{y^2}:\left( { - 2{x^2}y} \right)\) \( = 8{x^2} - 6xy - 4xy + 3{y^2} + 10xy\) \( = 8{x^2} + 3{y^2} + \left( {10xy - 6xy - 4xy} \right)\) \( = 8{x^2} + 3{y^2}\).

c) \[\frac{2}{{x - 2}} + \frac{3}{{x + 2}} + \frac{{5x - 18}}{{{x^2} - 4}}\]

\[ = \frac{2}{{x - 2}} + \frac{3}{{x + 2}} + \frac{{5x - 18}}{{\left( {x + 2} \right)\left( {x - 2} \right)}}\]

\[ = \frac{{2\left( {x + 2} \right)}}{{\left( {x + 2} \right)\left( {x - 2} \right)}} + \frac{{3\left( {x - 2} \right)}}{{\left( {x + 2} \right)\left( {x - 2} \right)}} + \frac{{5x - 18}}{{\left( {x + 2} \right)\left( {x - 2} \right)}}\]

\[ = \frac{{2\left( {x + 2} \right) + 3\left( {x - 2} \right) + 5x - 18}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\]

\[ = \frac{{2x + 4 + 3x - 6 + 5x - 18}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\]

\[ = \frac{{10x - 20}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\]\[ = \frac{{10(x - 2)}}{{\left( {x - 2} \right)\left( {x + 2} \right)}} = \frac{{10}}{{x + 2}}\].