Question

Cm \(\dfrac{a^3-4a^2-a+4}{a^3-7a^2+14a-8}\)=\(\dfrac{a+1}{a-2}\)

Answer 1

Có \(\text{VT }=\) \(\dfrac{a^3-4a^2-a+4}{a^3-7a^2+14a-8}\)

\(\Rightarrow VT=\dfrac{a^2\left(a-4\right)-\left(a-4\right)}{\left(a-2\right)\left(a^2+2a+4\right)-7a\left(a-2\right)}\)

\(\Rightarrow VT=\dfrac{\left(a-4\right)\left(a-1\right)\left(a+1\right)}{\left(a-2\right)\left(a^2-5a+4\right)}\)

\(\Rightarrow VT=\dfrac{\left(a+1\right)\left(a^2-5a+4\right)}{\left(a-2\right)\left(a^2-5a+4\right)}\)

\(\Rightarrow\dfrac{a+1}{a-2}\)

\(\Rightarrow VT=VP\)

\(\Rightarrowđpcm\)