Lời giải:
\(M=\frac{ab}{(c-a)(c-b)}+\frac{ac}{(b-a)(b-c)}+\frac{bc}{(a-b)(a-c)}\\ =\frac{-ab(a-b)}{(a-b)(b-c)(c-a)}+\frac{-ac(c-a)}{(a-b)(b-c)(c-a)}+\frac{-bc(b-c)}{(a-b)(b-c)(c-a)}\\ =\frac{-[ab(a-b)+ac(c-a)+bc(b-c)]}{(a-b)(b-c)(c-a)}\\ =\frac{(ab^2+bc^2+ca^2)-(a^2b+b^2c+c^2a)}{(ab^2+bc^2+ca^2)-(a^2b+b^2c+c^2a)}=1\)
Rut gon phan thuc
\(M=\frac{\left(b-c\right)^3+\left(c-a\right)^3+\left(a-b\right)^3}{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}\)
tính: \(\frac{1}{\left(b-c\right)\left(a^2+ac-b^2-bc\right)}+\frac{1}{\left(c-a\right)\left(b^2+ab-c^2-ac\right)}+\frac{1}{\left(a-b\right)\left(a^2+ab-c^2-bc\right)}\)
Tính (phân thức)
a)\(\frac{1}{\left(b-c\right)\left(a^2+ac-b^2-bc\right)}+\frac{1}{\left(c-a\right)\left(b^2+ab-c^2-ac\right)}+\frac{1}{\left(a-b\right)\left(c^2+bc-a^2-ab\right)}\)
Thực hiện phép tính :
\(\frac{1}{\left(b-c\right)\left(a^2+ac-b^2-bc\right)}+\frac{1}{\left(c-a\right)\left(b^2+ab-c^2-ac\right)}+\frac{1}{\left(a-b\right)\left(c^2+bc-a^2-ab\right)}\)
RUT GON PHAN THUC
1) \(\frac{\left(x-y\right)^3-3xy\left(x+y\right)+y^3}{x-6y}\)
2) \(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-c\right)}{ab^2-ac^2-b^3+bc^2}\)
3) \(\frac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)
Thực hiện phép tính
C=\(\frac{bc}{\left(a-b\right).\left(a-c\right)}+\frac{ac}{\left(b-a\right).\left(b-c\right)}+\frac{ab}{\left(c-a\right).\left(c-b\right)}\)
Rut gọn phân thức
\(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)
cho tam giác ABC, với AB=c, BC=a, AC=b, chứng minh rằng
\(\frac{a\left(b+c\right)\sqrt{bc\left(1-\frac{a^2}{b+c}\right)}+b\left(a+c\right)\sqrt{ac\left(1-\frac{b^2}{a+c}\right)}+c\left(a+b\right)\sqrt{ab\left(1-\frac{c^2}{a+b}\right)}}{a+b+c}\)
rút gọn bt
\(\frac{a^2-bc}{\left(a+b\right)\left(a+c\right)}+\frac{b^2-ac}{\left(a+b\right)\left(b+c\right)}+\frac{c^2-ab}{\left(a+c\right)\left(c+b\right)}\)
