Đáp án:
\(\dfrac{{4{x^3} + 20x - 100}}{{{{\left( {x - 5} \right)}^2}\left( {x + 5} \right)}}\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \pm 5\\
\dfrac{{12x - 10}}{{{{\left( {x - 5} \right)}^2}}} + \dfrac{{3x\left( {x + 5} \right) + \left( {x - 2} \right)\left( {x - 5} \right)}}{{\left( {x - 5} \right)\left( {x + 5} \right)}}\\
= \dfrac{{12x - 10}}{{{{\left( {x - 5} \right)}^2}}} + \dfrac{{3{x^2} + 15x + {x^2} - 7x + 10}}{{\left( {x - 5} \right)\left( {x + 5} \right)}}\\
= \dfrac{{12x - 10}}{{{{\left( {x - 5} \right)}^2}}} + \dfrac{{4{x^2} + 8x + 10}}{{\left( {x - 5} \right)\left( {x + 5} \right)}}\\
= \dfrac{{\left( {12x - 10} \right)\left( {x + 5} \right) + \left( {4{x^2} + 8x + 10} \right)\left( {x - 5} \right)}}{{{{\left( {x - 5} \right)}^2}\left( {x + 5} \right)}}\\
= \dfrac{{12{x^2} + 60x - 10x - 50 + 4{x^3} - 20{x^2} + 8{x^2} - 40x + 10x - 50}}{{{{\left( {x - 5} \right)}^2}\left( {x + 5} \right)}}\\
= \dfrac{{4{x^3} + 20x - 100}}{{{{\left( {x - 5} \right)}^2}\left( {x + 5} \right)}}
\end{array}\)
