Câu 3:
a) ĐKXĐ: \(x\ne\pm4;x\ne-1\)
b) \(A=\left(\dfrac{3}{x+4}-\dfrac{x-20}{x^2-16}\right).\dfrac{x-4}{x+1}\)
\(A=\left(\dfrac{3}{x+4}-\dfrac{x-20}{\left(x-4\right)\left(x+4\right)}\right).\dfrac{x-4}{x+1}\)
\(A=\left[\dfrac{3\left(x-4\right)-\left(x-20\right)}{\left(x-4\right)\left(x+4\right)}\right].\dfrac{x-4}{x+1}\)
\(A=\left[\dfrac{3x-12-x+20}{\left(x-4\right)\left(x+4\right)}\right].\dfrac{x-4}{x+1}\)
\(A=\left[\dfrac{2x+8}{\left(x-4\right)\left(x+4\right)}\right].\dfrac{x-4}{x+1}\)
\(A=\left[\dfrac{2\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}\right].\dfrac{x-4}{x+1}\)
\(A=\dfrac{2}{x-4}.\dfrac{x-4}{x+1}\)
\(A=\dfrac{2}{x+1}\)
c) Để A nhận được giá trị bằng 1 có:
\(A=\dfrac{2}{x+1}=1\Leftrightarrow x+1=2\Leftrightarrow x=1\)
Vậy khi x = 1 thì A nhận được giá trị bằng 1
