Question

Rút gọn phân thức

M=(\(\dfrac{4}{x-4}\)-\(\dfrac{4}{x+4}\)). \(\dfrac{x^2+8x+16}{32}\)

Answer 1

M = \(\left(\dfrac{4}{x-4}-\dfrac{4}{x+4}\right).\dfrac{x^2+8x+16}{32}\)

= \(\left(\dfrac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\dfrac{4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}\right).\dfrac{\left(x+4\right)^2}{32}\)

= \(\left(\dfrac{4x+16-4x+16}{\left(x-4\right)\left(x+4\right)}\right).\dfrac{\left(x+4\right)^2}{32}\)

= \(\dfrac{32}{x^2-16}.\dfrac{\left(x+4\right)^2}{32}\)

= \(\dfrac{\left(x+4\right)^2}{x^2-16}\) \(=\dfrac{x+4}{x-4}\)