Question

cho M= \(\dfrac{1}{x-2}-\dfrac{1}{x+2}+\dfrac{x^2+4x}{x^2-4}\)

rút gọn M

Answer 1

MTC = (x - 2)(x + 2)

\(M=\dfrac{1}{x-2}-\dfrac{1}{x+2}+\dfrac{x^2+4x}{x^2-4}\)

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

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

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

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

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