Ta có:\(\frac{a}{b}\)=\(\frac{a.\left(b+c\right)}{b.\left(b+c\right)}=\frac{a.b+ac}{b.\left(b+c\right)}\)
\(\frac{a+c}{b+c}=\frac{\left(a+c\right).b}{\left(b+c\right).b}=\frac{a.b+b.c}{b.\left(b+c\right)}\)
Vì \(\frac{a}{b}\)<1 =>a<b
=>a.c<b.c
=>a.b+a.c<a.b+b.c
=>\(\frac{a.b+a.c}{b.\left(a+b\right)}
\(CMR:\frac{a}{b}=\frac{c}{d}\ne thì\frac{a+b}{a-b}=\frac{c+d}{c-d}với:a,b,c,d\ne0\)
Cho \(\frac{a}{b}=\frac{c}{d}.CMR\frac{a^2+b^2}{b^2+c^2}=\frac{a}{c}\)
CMR: C=\(\frac{a}{a+b+c}+\frac{b}{b+c+d}+\frac{c}{c+d+a}+\frac{d}{d+a+b}\)không là số tự nhiên
Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)CMR \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\). Cmr: \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\)( b,d khác 0). CMR
a) \(\frac{a-b}{a}=\frac{c-d}{c}\)
b) \(\frac{a}{a+b}=\frac{c}{c+d}\)
c) \(\frac{a}{a-b}=\frac{c}{c-d}\)
Cho \(a,b\varepsilonℕ^∗\).CMR:\(\frac{a+b}{c}+\frac{c+b}{a}+\frac{a+c}{b}\ge b\)
Với a, b, c, d >0 CMR 1<\(\frac{a}{b+c+d}+\frac{b}{c+d+a}+\frac{c}{b+c+d}+\frac{d}{a+b+c}< 2\)
Cho \(\frac{a}{b}=\frac{c}{d}\). CMR \(\frac{a+b}{a-b}=\frac{c+d}{c-d}\)
CHO a,b,c thuoc N CMR :\(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{a+c}\)la so tu nhien