Question

rút gọn
a) a^3 - 3a^2+ 2a - 6 / a^2 + 2

b)(a-b)(c-d) / (b^2 - a^2)(d^2 - c^2 )

Answer 1

a)

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

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

b)\(\dfrac{\left(a-b\right)\left(c-d\right)}{\left(b^2-a^2\right)\left(d^2-c^2\right)}=\dfrac{\left(a-b\right)\left(c-d\right)}{\left(a^2-b^2\right)\left(c^2-d^2\right)}\)

\(\dfrac{\left(a-b\right)\left(c-d\right)}{\left(a-b\right)\left(a+b\right)\left(c-d\right)\left(c+d\right)}=\dfrac{1}{\left(a+b\right)\left(c+d\right)}\)

Answer 2

\(a,\dfrac{a^3-3a^2+2a-6}{a^2+2}\)

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

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

\(=a-3\)

\(b,\dfrac{\left(a-b\right)\left(c-d\right)}{\left(b^2-a^2\right)\left(d^2-c^2\right)}\)

\(=\dfrac{\left(a-b\right)\left(c-d\right)}{\left(a^2-b^2\right)\left(c^2-d^2\right)}\)

\(=\dfrac{\left(a-b\right)\left(c-d\right)}{\left(a-b\right)\left(a+b\right)\left(c-d\right)\left(c+d\right)}\)

\(=\dfrac{1}{\left(a+b\right)\left(c+d\right)}\)