Question

a, Thực hiện phép tính: \(\dfrac{3x-8}{x-2}\) + \(\dfrac{5-x}{2-x}\) + \(\dfrac{2x+1}{x-2}\)

b, Rút gọn biểu thức: A = \(\dfrac{x^2-2x+1}{x^2-1}\)

Answer 1

a.

\(\dfrac{3x-8}{x-2}+\dfrac{5-x}{2-x}+\dfrac{2x+1}{x-2}\)

\(=\dfrac{3x-8}{x-2}-\dfrac{5-x}{x-2}+\dfrac{2x+1}{x-2}=\dfrac{3x-8-5+x+2x+1}{x-2}=\dfrac{6x-12}{x-2}=\dfrac{6\left(x-2\right)}{x-2}=6\)

b.

\(A=\dfrac{x^2-2x+1}{x^2-1}=\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}=\dfrac{x-1}{x+1}\)

Answer 2

a)

\(\dfrac{3x-8}{x-2}+\dfrac{5-x}{2-x}+\dfrac{2x+1}{x-2}\\ =\dfrac{3x-8+x-5+2x+1}{x-2}\\ =\dfrac{6x-12}{x-2}\\ =\dfrac{6\left(x-2\right)}{x-2}\\ =6\)

b)

\(A=\dfrac{x^2-2x+1}{x^2-1}\\ A=\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x+1\right)}\\ A=\dfrac{x-1}{x+1}\)