B1: Rút gọn phân thức
Q=a^2(b-c)+b^2(c-a)+c^2(a-b)/ab^2-ac^2-b^3+bc^2
B2: Rút gọn các phân thức a)a^2n-b^2n/(a-b(a^n+b^n)
bx^3n-y^3n/x^n-y^n
1.
$Q=\dfrac{a^2(b-c)+b^2(c-a)+c^2(a-b)}{ab^2-ac^2-b^3+bc^2}
\\=\dfrac{a^2b-a^2c+b^2c-ab^2+c^2(a-b)}{(ab^2-b^3)-(ac^2-bc^2)}
\\=\dfrac{(a^2b-ab^2)-(a^2c-b^2c)+c^2(a-b)}{b^2(a-b)-c^2(a-b)}
\\=\dfrac{ab(a-b)-c(a+b)(a-b)+c^2(a-b)}{(a-b)(b^2-c^2)}
\\=\dfrac{(a-b)(ab-ac-bc+c^2)}{(a-b)(b-c)(b+c)}
\\=\dfrac{(a-b)[a(b-c)-c(b-c)]}{(a-b)(b-c)(b+c)}
\\=\dfrac{(a-b)(b-c)(a-c)}{(a-b)(b-c)(b+c)}
\\=\dfrac{a-c}{b+c}$
2. Với $n\in \mathbb{N^*}$ ta có:
a) $\dfrac{a^{2n}-b^{2n}}{(a-b)(a^n+b^n)}=\dfrac{(a^n-b^n)(a^n+b^n)}{(a-b)(a^n+b^n)}$
$=\dfrac{(a-b)(a^{n-1}+a^{n-2}.b+...+a.b^{n-2}+b^{n-1})}{a-b}$
$=a^{n-1}+a^{n-2}.b+...+a.b^{n-2}+b^{n-1}$
b) $\dfrac{x^{3n}-y^{3n}}{x^n-y^n}=\dfrac{(x^n-y^n)(x^{2n}+x^ny^n+y^{2n})}{x^n-y^n}=x^{2n}+x^ny^n+y^{2n}$
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
