\(\dfrac{x+7}{x^2-x-6}+\dfrac{x+10}{x^2+x-2}+\dfrac{x+7}{x^2-4x+3}\)
\(=\dfrac{x+7}{x^2+2x-3x-6}+\dfrac{x+10}{x^2+2x-x-2}+\dfrac{x+7}{x^2-x-3x+3}\)
\(=\dfrac{x+7}{\left(x-3\right)\left(x+2\right)}+\dfrac{x+10}{\left(x-1\right)\left(x+2\right)}+\dfrac{x+7}{\left(x-3\right)\left(x-1\right)}\)
\(=\dfrac{\left(x+7\right)\left(x-1\right)}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}+\dfrac{\left(x+10\right)\left(x-3\right)}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}\)
+\(\dfrac{\left(X+7\right)\left(x+2\right)}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}\)
=\(\dfrac{x^2-x+7x-7+x^2-3x+10-30+x^2+2x+7x+14}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}\)
\(=\dfrac{3x^2+12x-13}{\left(x-1\right)\left(x-3\right)\left(x+2\right)}\)
Rút gọn đến đây là tối giản rồi nhé ^^
\(=\dfrac{x+7}{\left(x-3\right)\left(x+2\right)}+\dfrac{x+10}{\left(x-1\right)\left(x+2\right)}+\dfrac{x-7}{\left(x-1\right)\left(x-3\right)}\)
\(=\dfrac{\left(x+7\right)\left(x-1\right)+\left(x+10\right)\left(x-3\right)+\left(x-7\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{3x^2+8x-51}{\left(x-1\right)\left(x+2\right)\left(x-3\right)}\)
\(=\dfrac{x+\dfrac{17}{3}}{\left(x-1\right)\left(x+2\right)}\)
