Theo đề ra\(\Rightarrow\frac{a+b-c}{c}+2=\frac{b+c-a}{a}+2=\frac{c+a-b}{b}+2\)
\(\Rightarrow\frac{a+b+c}{c}=\frac{a+b+c}{a}=\frac{a+b+c}{b}\)
Mà: a + b + c khác 0 => a = b = c
=> P = (1 + 1)(1 + 1)(1 + 1) = 2 . 2 . 2 = 8
cho a,b,c thỏa mãn : \(\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-a\right)\left(b-c\right)}+\frac{a-b}{\left(c-b\right)\left(c-a\right)}=2013\)
tính M = \(\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\)
Cho a,b,c khác 0 và \(\frac{a+b-c}{c}=\frac{b+c-a}{a}=\frac{c+a-b}{b}\)
Tính P = \(\left(1+\frac{b}{a}\right)\left(1+\frac{c}{b}\right)\left(1+\frac{a}{c}\right)\)
cho a,b,c là các số thực khác 0 thỏa mãn \(\frac{a+b-c}{c}=\frac{b+c-a}{a}=\frac{c+a-b}{b}\text{. Tính P}=\left(1+\frac{b}{a}\right)\left(1+\frac{a}{c}\right)\left(1+\frac{c}{b}\right)\)
Cho a,b ,c đều khác 0 và a+b+c khác 0
\(\frac{a+b-c}{c}=\frac{b+c-a}{a}=\frac{c+a-b}{b}\)
Tính M= (\(\left(1+\frac{b}{a}\right).\left(1+\frac{a}{c}\right).\left(1+\frac{c}{b}\right)\)
CMR
\(\frac{1}{2}\left[\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-c\right)\left(b-a\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}\right]=\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\)
Cho a,b,c khác 0 thỏa mãn \(\frac{a-b+c}{2b}=\frac{c-a+b}{2a}=\frac{a-c+b}{2c}\). Tính \(P=\left(1+\frac{c}{b}\right)\left(1+\frac{b}{a}\right)\left(1+\frac{a}{c}\right)\)
Cho a,b,c\(\ne\)0,\(\frac{a+b-c}{c}=\frac{b+c-a}{a}=\frac{a+a-b}{b}\)
Tính D=\(\left(1+\frac{b}{a}\right)\left(1+\frac{c}{b}\right)\left(1+\frac{a}{c}\right)\)
Cho 3 số a,b,c đôi một phân biệt. CMR:
\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-c\right)\left(b-a\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}=2\left(\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\right)\\ \)
Cho a,b,c thỏa mãn:
\(\frac{b-c}{\left(a-b\right)\left(a-c\right)}+\frac{c-a}{\left(b-c\right)\left(b-a\right)}+\frac{a-b}{\left(c-a\right)\left(c-b\right)}\)= 2013
Tính giá trị biểu thức:
\(\frac{1}{a-b}+\frac{1}{b-c}+\frac{1}{c-a}\)
