Rút gọn biểu thức x^2 / (5x + 25) + (2x - 10) / x + (50 + 5x)
Giải thích
\(\frac{{{x^2}}}{{5x + 25}} + \frac{{2x - 10}}{x} + \frac{{50 + 5x}}{{{x^2} + 5x}}\)
\( = \frac{{{x^3}}}{{5x\left( {x + 5} \right)}} + \frac{{5\left( {2x - 10} \right)\left( {x + 5} \right)}}{{5x\left( {x + 5} \right)}} + \frac{{5\left( {50 + 5x} \right)}}{{5x\left( {x + 5} \right)}}\)
\( = \frac{{{x^3} + 10\left( {x - 5} \right)\left( {x + 5} \right) + 250 + 25x}}{{5x\left( {x + 5} \right)}}\)
\( = \frac{{{x^3} + 10\left( {{x^2} - 25} \right) + 250 + 25x}}{{5x\left( {x + 5} \right)}}\)
\( = \frac{{{x^3} + 10{x^2} + 25x}}{{5x\left( {x + 5} \right)}}\)
\( = \frac{{x\left( {{x^2} + 10x + 25} \right)}}{{5x\left( {x + 5} \right)}}\)
\( = \frac{{x{{\left( {x + 5} \right)}^2}}}{{5x\left( {x + 5} \right)}}\)
\( = \frac{{x + 5}}{5}\).