Question

Bài 3: Chứng tỏ hai phân thức sau bằng nhau

a)m+1/m-1 và m²+2m+1/m²-1

b)2a⁴+3a³+2a+3/(a²-a+1)(4a+6) và a+1/2

Answer 1

a) Ta có: \(\dfrac{m^2+2m+1}{m^2-1}\)

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

\(=\dfrac{m+1}{m-1}\)

b) Ta có: \(\dfrac{2a^4+3a^3+2a+3}{\left(a^2-a+1\right)\left(4a+6\right)}\)

\(=\dfrac{a^3\left(2a+3\right)+\left(2a+3\right)}{\left(a^2-a+1\right)\left(4a+6\right)}\)

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

\(=\dfrac{a+1}{2}\)