Question

cho các phân thức sau:

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

B= \(\dfrac{x^2-9}{x^2-6x+9}\)

a,tìm ĐKXĐ . rút gọn

b, tìm x để các biểu thức trên bằng 0

Answer 1

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

ĐKXĐ: \(\left\{{}\begin{matrix}x\ne-3\\x\ne2\end{matrix}\right.\)

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

\(A=0\Leftrightarrow\dfrac{2}{x-2}=0\Leftrightarrow2=0\) (vô lí)

Vậy \(x\in\varnothing\)

\(B=\dfrac{x^2-9}{x^2-6x+9}\)

ĐKXĐ: \(x\ne2\)

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

\(B=0\Leftrightarrow x+3=0\Leftrightarrow x=-3\)

Vậy x = -3 thì B = 0