\(\frac{2x-9}{x^2-5x+6}-\frac{x+3}{x-2}-\frac{2x+1}{3-x}\)
\(=\frac{2x-9}{x^2-2x-3x+6}-\frac{\left(x+3\right)\left(x-3\right)}{\left(x-2\right)\left(x-3\right)}+\frac{\left(2x+1\right)\left(x-2\right)}{\left(x-3\right)\left(x-2\right)}\)
\(=\frac{2x-9}{x\left(x-2\right)-3\left(x-2\right)}-\frac{x^2-9}{\left(x-2\right)\left(x-3\right)}+\frac{2x^2-3x-2}{\left(x-3\right)\left(x-2\right)}\)
\(=\frac{2x-9-x^2+9+2x^2-3x-2}{\left(x-2\right)\left(x-3\right)}\)
\(=\frac{x^2-x-2}{\left(x-2\right)\left(x-3\right)}\)
\(=\frac{x^2-2x+x-2}{\left(x-2\right)\left(x-3\right)}\)
\(=\frac{x\left(x-2\right)+\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\)
\(=\frac{\left(x-2\right)\left(x+1\right)}{\left(x-2\right)\left(x-3\right)}=\frac{x+1}{x-3}\)
x^2-5x+6= (x-2)(x-3)
Áp dụng vào biểu thức ta đc
\(=(2x+9)/((x-2)(x-3))-((x+3)(x-3)/((x-2)x-3))+((2x+1)(x-2))/((x-3)(x-2)\)
=(2x+9-x^2+9+2x^2-3x-2)/(x-2)(x-3)
=(16-x+x^2)/(x-2)(x-3)
con lại bạn tự khai triển ra nhé!
