Thực hiện phép cộng: 6/x^2 + 4x + 3/2x + 8

Trả lời

Lời giải

Ta có \(\frac{6}{{{x^2} + 4x}} + \frac{3}{{2x + 8}} = \frac{6}{{\left( {x + 4} \right)x}} + \frac{3}{{2\left( {x + 4} \right)}}\)

\( = \frac{{6\,.\,2}}{{2\left( {x + 4} \right)x}} + \frac{{3x}}{{2x\left( {x + 4} \right)}}\)

\( = \frac{{12}}{{2x\left( {x + 4} \right)}} + \frac{{3x}}{{2x\left( {x + 4} \right)}}\)

\( = \frac{{12 + 3x}}{{2x\left( {x + 4} \right)}} = \frac{{3\left( {x + 4} \right)}}{{2x\left( {x + 4} \right)}} = \frac{3}{{2x}}\).