Bài 18 trang 43 SGK Toán 8 tập 1

Quy đồng mẫu thức hai phân thức:

a) \(\dfrac{{3x}}{{2x + 4}}\) và \(\dfrac{{x + 3}}{{{x^2} - 4}}\)

b) \(\dfrac{{x + 5}}{{{x^2} + 4x + 4}}\) và \(\dfrac{x}{{3x + 6}}\)

a) Ta có: \(2x + 4 =2(x+2)\)

\({x^2} - 4 = \left( {x - 2} \right)\left( {x + 2} \right)\)

\(MTC = 2\left( {x - 2} \right)\left( {x + 2} \right) = 2\left( {{x^2} - 4} \right)\)

Quy đồng:

\(\dfrac{{3x}}{{2x + 4}} = \dfrac{{3x\left( {x - 2} \right)}}{{2\left( {x + 2} \right)\left( {x - 2} \right)}} = \dfrac{{3x\left( {x - 2} \right)}}{{2\left( {{x^2} - 4} \right)}}\)

\(\dfrac{{x + 3}}{{{x^2} - 4}} = \dfrac{{\left( {x + 3} \right).2}}{{\left( {x - 2} \right)\left( {x + 2} \right).2}} = \dfrac{{2\left( {x + 3} \right)}}{{2\left( {{x^2} - 4} \right)}}\)

b) Ta có:

\({x^2} + 4x + 4  = {x^2} + 2.x.2 + {2^2}= {\left( {x + 2} \right)^2}\)

\(3x + 6 = 3\left( {x + 2} \right)\)

MTC = \(3{\left( {x + 2} \right)^2}\)

Quy đồng:

 \(\dfrac{{x + 5}}{{{x^2} + 4x + 4}} = \dfrac{{\left( {x + 5} \right).3}}{{{{\left( {x + 2} \right)}^2}.3}} = \dfrac{{3\left( {x + 5} \right)}}{{3{{\left( {x + 2} \right)}^2}}}\)

\(\dfrac{x}{{3x + 6}} = \dfrac{{x.\left( {x + 2} \right)}}{{3\left( {x + 2} \right).\left( {x + 2} \right)}} = \dfrac{{x\left( {x + 2} \right)}}{{3{{\left( {x + 2} \right)}^2}}}\)