Question

Cho biểu thức \(\dfrac{x\left(x-4\right)+4}{x^2-4}\)

a) Rút gọn P

b) Tìm x để P= \(\dfrac{1001}{1003}\)

Answer 1

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

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

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

\(P=\dfrac{x-2}{x+2}\)

b) \(P=\dfrac{x-2}{x+2}\)=\(\dfrac{1001}{1003}\)

\(=>1003x-2006=1001x+2002\)

\(2x=4008=>x=2004\)

Answer 2

a) ĐK: \(x\ne2;x\ne-2\)
\(P=\dfrac{x\left(x-4\right)+4}{x^2-4} =\dfrac{x^2-4x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{\left(x-2\right)^2}{\left(x-2\right)\left(x+2\right)}=\dfrac{x-2}{x+2}\)

b) \(P=\dfrac{1001}{1003}\Leftrightarrow\dfrac{x-2}{x+2}=\dfrac{1001}{1003}\Rightarrow1003x-2006=1001x+2002\)
\(\Leftrightarrow2x=4008\Leftrightarrow x=2004\) (tmđk)