Làm các phép tính sau:
a)\({{4xy - 5} \over {10{x^3}y}} - {{6{y^2} - 5} \over {10{x^3}y}};\)
b)\({{7x + 6} \over {2x\left( {x + 7} \right)}} - {{3x + 6} \over {2{x^2} + 14x}}\)
Hướng dẫn làm bài:
a)\({{4xy - 5} \over {10{x^3}y}} - {{6{y^2} - 5} \over {10{x^3}y}} = {{4xy - 5 - \left( {6{y^2} - 5} \right)} \over {10{x^3}y}}\)
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\( = {{4xy - 5 - 6{y^2} + 5} \over {10{x^3}y}} = {{4xy - 6{y^2}} \over {10{x^3}y}}\)
\( = {{2y\left( {2x - 3y} \right)} \over {10{x^3}y}} = {{2x - 3y} \over {5{x^3}}}\)
b)\({{7x + 6} \over {2x\left( {x + 7} \right)}} - {{3x + 6} \over {2{x^2} + 14x}} = {{7x + 6} \over {2x\left( {x + 7} \right)}} + {{ - \left( {3x + 6} \right)} \over {2x\left( {x + 7} \right)}}\)
\( = {{7x + 6 - 3x - 6} \over {2x\left( {x + 7} \right)}} = {{4x} \over {2x\left( {x + 7} \right)}} = {2 \over {x + 7}}\)