Question

rút gọn biểu thức:

D=\(\dfrac{5}{2x^2+6x}-\dfrac{4-3x^2}{x^2-9}\)- 3

 

Answer 1

\(D=\dfrac{5}{2x^2+6x}-\dfrac{4-3x^2}{x^2-9}-3\) (đk:\(x\ne3;x\ne-3\))

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

\(=\dfrac{5\left(x-3\right)}{2x\left(x-3\right)\left(x+3\right)}-\dfrac{\left(4-3x^2\right).2x}{2x\left(x-3\right)\left(x+3\right)}-\dfrac{3.2x\left(x-3\right)\left(x+3\right)}{2x\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{5x-15-8x+6x^3-6x\left(x^2-9\right)}{2x\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{51x-15}{2x\left(x-3\right)\left(x+3\right)}\)