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cho phan thuc :\(\frac{x^2-10x+25}{x^2-5x}\)\(\left(x\ne0;x\ne5\right)\)
a) Rut gon phan thuc
b) Tim x de phan thuc co gia tri bang 0
c) Tim x de phan thuc co gia tri bang \(\frac{5}{2}\)
Cho a,b,c la 3 so thuc phan biet tong bang 0
a) s= a^3 / (a-b)(a-c) + b^3 / (b-c)(b-a) + c^3/ (c-a)(c-b)
b) a(b^2 +c^2) +b (c^2 + a^2) + C(a^2 + b^2) +3abc
Bai 2: cho a,b,c>0.CMR
\(\frac{a^3}{bc}+\frac{b^3}{ac}+\frac{c^3}{ab}\)lon hon hoac bang a+b+c
tinh gia tri cua bieu thuc A=\(\left(\frac{a-b}{c}+\frac{b-c}{a}+\frac{c-a}{b}\right)\))\(\left(\frac{c}{a-b}+\frac{a}{b-c}+\frac{b}{c-a}\right)\). cho biet a+b+c=0
cho phan thuc \(\frac{x+1}{x^2+x}\)
a) tim dieu kien cua x de gia tri phan thuc duoc xac dinh
b) rut gon phan thuc
c) tinh gia tri phan thuc tai x = 2014
cho 3 so thuc duong a,b,c .TM : a+b+c \(\le\)3
CMR \(\frac{1}{a^{2+}+b^2+c^2}\)+ \(\frac{2012}{ab+bc+ac}\)\(\ge\)671
Cho 3 so thuc a b c \(\ne0\)thoa man \(\left(a+b+c\right)^2=a^2+b^2+c^2\). CMR
\(\frac{a^2}{a^2+2bc}+\frac{b^2}{b^2+2ac}+\frac{c^2}{c^2+2ab}=\frac{bc}{a^2+2bc}+\frac{ac}{b^2+2ac}+\frac{ab}{c^2+2ab}\)
Cho a,b,c > 0 . CMR:
\(\frac{a+b}{bc+a^2}+\frac{b+c}{ac+b^2}+\frac{c+a}{ab+c^2}\le\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\\ \)
1. cho a,b,c > 0.CMR :\(\frac{bc}{a}+\frac{ac}{b}+\frac{ab}{c}\ge a+b+c\)\(c\)
2. cho a,b,c là 3 cạnh của tam giác cmr: \(1< \frac{a}{bc}+\frac{b}{c+a}+\frac{c}{a+b}< 2\)