Đặt :
\(\dfrac{a}{b}=\dfrac{c}{d}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\d=ck\end{matrix}\right.\)
Ta có :
\(\dfrac{a}{a-b}=\dfrac{bk}{bk-b}=\dfrac{bk}{b\left(k-1\right)}=\dfrac{k}{k-1}\left(1\right)\)
\(\dfrac{c}{c-d}=\dfrac{dk}{dk-d}=\dfrac{dk}{d\left(k-1\right)}=\dfrac{k}{k-1}\left(2\right)\)
Từ \(\left(1\right)+\left(2\right)\Leftrightarrowđpcm\)
Bài 1: CMR : Nếu a2 = b.c thì \(\dfrac{a+b}{a-b}=\dfrac{c+a}{c-a}\) Đảo lại có đúng không?
Bài 2: Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) CMR: \(\left(\dfrac{a+b+c}{b+c+d}\right)\)3 =\(\dfrac{a}{d}\)
Bài 3: Cho dãy tỉ số: \(\dfrac{b.z-c.y}{a}=\dfrac{c.x-a.z}{b}=\dfrac{a.y-b.x}{c}\) , CMR: \(\dfrac{x}{a}=\dfrac{y}{b}=\dfrac{z}{c}\)
\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}.CMR\left(\dfrac{a+b+c}{b+c+d}\right)^3=\dfrac{a}{d}\)
Bài 1
CMR: \(\dfrac{a}{c}=\dfrac{c}{b}=\dfrac{b}{d}cmr:\dfrac{a^3+c^3-b^3}{c^3+b^3-d^3}=\dfrac{a}{d}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d}.CMR\)
a, \(\dfrac{a+c}{b+d}=\dfrac{a-c}{b-d}\)
b, \(\dfrac{c}{a+c}=\dfrac{b}{b+d}\)
c, \(\dfrac{a+b}{a}=\dfrac{d}{c+d}\)
d, \(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)
e, \(\dfrac{4a-3b}{a}=\dfrac{4c-3d}{c}\)
f, \(\dfrac{a^2+b^2}{a^2-b^2}=\dfrac{c^2+d^2}{c^2-d^2}\)
cho \(\dfrac{a}{b}=\dfrac{c}{d}\), cmr: \(\dfrac{a}{b}=\dfrac{a+c}{b+d}\)
cho \(\dfrac{a}{b}=\dfrac{c}{d}\).CMR:
a) \(\dfrac{a-b}{a}=\dfrac{c-d}{c}\)
b) \(\dfrac{a-b}{c-d}=\dfrac{a^2-b^2}{c^2-d^2}\)
c) \(\dfrac{\left(a+b\right)^2}{\left(c+d\right)^2}=\dfrac{a^2+b^2}{c^2+d^2}\)
d) \(\dfrac{7a^2+5ac}{7a^2-5ac}=\dfrac{2b^2+5bd}{7b^2-5bd}\)
Cho M = \(\dfrac{a}{a+b+c}+\dfrac{b}{a+b+d}+\dfrac{c}{b+c+d}+\dfrac{d}{a+d+c}\) (a,b,c thuộc N sao)
CMR: M ko là số tự nhiên
cho \(\dfrac{b}{a}=\dfrac{c}{d}\)cmr:
a,\(\dfrac{a}{a-b}=\dfrac{c}{c-d}\)
b,\(\dfrac{a}{b}=\dfrac{a+c}{b+d}\)
c,\(\dfrac{a}{3a+b}=\dfrac{c}{3c+d}\)
d,\(\dfrac{ac}{bd}=\dfrac{a^2+b^2}{b^2+d^2}\)
e,\(\dfrac{a.b}{c.d}=\dfrac{a^2-b^2}{c^2-d^2}\)
f,\(\dfrac{a.b}{c.d}=\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)
Cho tỉ lệ thức \(\dfrac{a}{b}=\dfrac{c}{d}\)
CMR:\(\dfrac{a-b}{a+b}=\dfrac{c-d}{c+d}\)
