Question

a. rút gọn phân thức: P= \(\dfrac{x^{2^{ }}+2x+1}{x^{2^{ }}-1}\)

b.thực hiện phép tính: \(\dfrac{8-x}{\left(x+2_{^{ }}\right)\left(x-3\right)}+\dfrac{2}{x+2}\)

Answer 1

a) \(P=\dfrac{x^2+2x+1}{x^2-1}\)

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

b) \(\dfrac{8-x}{\left(x+2\right)\left(x-3\right)}+\dfrac{2}{x+2}\)

\(=\dfrac{8-x}{\left(x+2\right)\left(x-3\right)}+\dfrac{2\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}\)

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

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

\(=\dfrac{1}{x-3}\)

Answer 2

a)

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

b)

\(\dfrac{8-x}{\left(x+2\right)\left(x-3\right)}\)+\(\dfrac{2}{x+2}\)

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

= \(\dfrac{x+2}{\left(x+2\right)\left(x-3\right)}\) = \(\dfrac{1}{x-3}\)