Rút gọn
( a + b + c ) (a^2 + b^2 + c^2 - ab - ac - bc )
Rút gọn : \(P=\frac{bc-a^2+ac-b^2+ab-c^2}{a\left(bc-a^2\right)+b\left(ac-b^2\right)+c\left(ab-c^2\right)}\)
Rút gọn phân thức:
(a^2+b^2+c^2)(a+b+c)+(ab+ac+bc)/(a+b+c)^2-(ab+bc+ca)
Sửa đề:
\(\frac{\left(a^2+b^2+c^2\right)\left(a+b+c\right)+\left(ab+bc+ca\right)\left(a+b+c\right)}{\left(a+b+c\right)^2-\left(ab+bc+ca\right)}\)
\(=\frac{\left(a^2+b^2+c^2+ab+bc+ca\right)\left(a+b+c\right)}{a^2+b^2+c^2+2ab+2bc+2ca-\left(ab+bc+ca\right)}\)
\(=\frac{\left(a^2+b^2+c^2+ab+bc+ca\right)\left(a+b+c\right)}{a^2+b^2+c^2+ab+bc+ca}\)
\(=a+b+c\left(a^2+b^2+c^2+ab+bc+ca\ne0\right)\)
(a^2+b^2+c^2)(a+b+c)+(ab+ac+bc)^2/(a+b+c)^2-(ab+bc+ca) có đúng đề ko ạ
Rút gọn
\(\dfrac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)
Lời giải:
\(\frac{a^2(b-c)+b^2(c-a)+c^2(a-b)}{ab^2-ac^2-b^3+bc^2}=\frac{a^2(b-c)-b^2[(b-c)+(a-b)]+c^2(a-b)}{a(b^2-c^2)-b(b^2-c^2)}\)
\(=\frac{(a^2-b^2)(b-c)-(b^2-c^2)(a-b)}{(a-b)(b^2-c^2)}=\frac{(a-b)(b-c)(a+b-b+c)}{(a-b)(b-c)(b+c)}=\frac{(a-b)(b-c)(a-c)}{(a-b)(b-c)(b+c)}\)
\(=\frac{a-c}{b+c}\)
Ta có: \(\dfrac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)
\(=\dfrac{a^2\left(b-c\right)-b^2\left[\left(b-c\right)+\left(a-b\right)\right]+c^2\left(a-b\right)}{a\left(b^2-c^2\right)-b\left(b^2-c^2\right)}\)
\(=\dfrac{a^2\left(b-c\right)-b^2\left(b-c\right)-b^2\left(a-b\right)+c^2\left(a-b\right)}{\left(b^2-c^2\right)\left(a-b\right)}\)
\(=\dfrac{\left(b-c\right)\left(a^2-b^2\right)-\left(a-b\right)\left(b^2-c^2\right)}{\left(b-c\right)\left(b+c\right)\left(a-b\right)}\)
\(=\dfrac{\left(b-c\right)\left(a-b\right)\left(a+b\right)-\left(a-b\right)\left(b-c\right)\left(b+c\right)}{\left(b-c\right)\left(b+c\right)\left(a-b\right)}\)
\(=\dfrac{\left(a-b\right)\left(b-c\right)\left(a+b-b-c\right)}{\left(b-c\right)\left(a-b\right)\left(b+c\right)}\)
\(=\dfrac{a-c}{b+c}\)
Bài 1: Cho a+b+c=0; rút gọn biểu thức A= a^2/(a^2-b^2-c^2) + b^2/(b^2-c^2-a^2) + c^2/(c^2-b^2-a^2)
Bài 2: Cho abc=2; rút gọn A= a/(ab+a+2) + b/(bc+b+1) + 2c/(ac+2c+2)
Rút gọn M= (a2-bc)/((a+b)(a+c)) + (b2-ac)/((b+a)(b+c) + (c2 -ab)/((a+c)(a+b))
cho (a+b+c)^2 = a^2 + b^2 +c^2 và abc khác 0
cmr bc/a^2 + ac/b^2 +ab/c^2 = 3
cho abc=1. rút gọn
a/ab+a+1 + b/bc+b+1 + c/ca+c+1
Rút gọn:
\(\left(a+b+c\right)\left(a^2+b^2+c^2-ab-ac-bc\right)\)
Rút gọn biểu thức:
M= a/(ab+a+2)+b/(bc+b+1)+c/(ac+2c+2). Biết abc=2
Cho phân thức
M=(a2+b2+c2)(a+b+c)2+(ab+bc+ac)2/(a+b+c)2-(ab+bc+ac)
a)Tìm giá trị của a,b,c để phân thức được xác định
b)Rút gọn phân thức M