a) Cho \(\dfrac{a}{b}=\dfrac{c}{d}\) (\(a,b,c,d\ne0\)). Chứng minh rằng:

1) \(\dfrac{2a+5b}{3a-4b}=\dfrac{2c+5d}{3c-4d}\)

2) \(\dfrac{ab}{cd}=\dfrac{a^2+b^2}{c^2+d^2}\)

3) \(\dfrac{a^3+b^3}{c^3+d^3}=\dfrac{\left(a+b\right)^3}{\left(c+d\right)^3}\) \(\left(\dfrac{a}{b}=\dfrac{c}{d}\ne1\right)\)

b)Cho \(\dfrac{2a+13b}{3a-7b}=\dfrac{2c+13d}{3c-7d}\). Chứng minh rằng:\(\dfrac{a}{b}=\dfrac{c}{d}\)

c)Cho \(\dfrac{cy-bz}{x}=\dfrac{az-cx}{y}=\dfrac{bx-ay}{z}\). Chứng minh rằng: \(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)

Cho \(\dfrac{a}{b}\)=\(\dfrac{c}{d}\) chứng minh rằng:

a) \(\dfrac{a}{a-b}\)=\(\dfrac{c}{c-d}\)

b) \(\dfrac{a}{b}\)=\(\dfrac{a+c}{b+d}\)

c)\(\dfrac{a}{3a+b}\)=\(\dfrac{c}{3c+b}\)

d) \(\dfrac{a.c}{b.c}\)=\(\dfrac{a^2+c^2}{b^2+d^2}\)

e) \(\dfrac{a.b}{c.d}\)=\(\dfrac{a^2-b^2}{c^2-d^2}\)

f) \(\dfrac{a.b}{c.d}\)=\(\dfrac{\left(a-b\right)^2}{\left(c-d\right)^2}\)

a ) Tìm x để : \(\frac{x^2-1}{x^2}\le0\)

b ) Cho \(\frac{a^2+b^2}{c^2+d^2}=\frac{qb}{cd}\) a ,b , c , d \(\ne\) 0 , c \(\ne\) + d . Chứng minh : \(\frac{a}{b}=\frac{c}{d}\) hoặc \(\frac{a}{b}=\frac{d}{c}\)

c ) Cho P = \(\frac{5}{\sqrt{x}-3}\) . Tìm x \(\in\) Z để P \(\in\) Z

bài 1 :

a)\(\dfrac{3}{7}\) + ( -\(\dfrac{5}{2}\) ) + ( \(\dfrac{-3}{5}\) ) b) ( -\(\dfrac{4}{3}\) ) + (-\(\dfrac{2}{5}\) ) + (- \(\dfrac{3}{2}\) )

c) \(\dfrac{4}{5}\)- ( \(\dfrac{-2}{7}\) ) - ( \(\dfrac{7}{10}\) ) d ) \(\dfrac{2}{3}\) - [(-\(\dfrac{4}{7}\) ) - ( \(\dfrac{1}{2}\) + \(\dfrac{3}{8}\) )]

bài 2 : tìm x , biêt

a) x + \(\dfrac{1}{3}\) = \(\dfrac{3}{4}\) ; b) x- \(\dfrac{2}{5}\) = \(\dfrac{5}{7}\)

c) -x - \(\dfrac{2}{3}\) = - \(\dfrac{6}{7}\) d) \(\dfrac{4}{7}\) -x = \(\dfrac{1}{3}\)

( mai nộp bài rôi ai giúp vs )

Bài 1,\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\). Chứng minh rằng: \(\frac{a}{b}=\frac{5}{6}\)

Bài 3, Bốn số a, b,c,d thỏa mãn điều kiện:\(b^2=ac;c^2=bd.\)Chứng minh:\(\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\frac{a}{d}\)

Bài 2, Chứng minh rằng nếu: \(\frac{a}{b}=\frac{c}{d}\) thì \(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)

Cho \(\dfrac{a}{b} = \dfrac{c}{d}\) . Chứng minh :

a, \(\dfrac{a^{2005}}{b^{2005}} = \dfrac{(a-c)^{2005}}{(b-d)^{2005}}\)

b, \(\dfrac{(a^2+b^2)^3}{(c^2+d^2)^3}\) =\(\dfrac{a^3+b^3)^2}{(c^3+d^3)^2}\)

c, \((\dfrac{a-b}{c-d})^{2005}\) = \(\dfrac{2.a^{2005}-b^{2005}}{2.c^{2005}-d^{2005}}\)

d, \(\dfrac{(a^2-b^2)^5}{(c^2-d^2)^5} = \) \(\dfrac{a^{10}+b^{10}}{c^{10}+d^{10}}\)

e, \(\dfrac{2.a^{2005}+5.b^{2005}}{2.c^{2005}+5.d^{2005}}\) = \(\dfrac{(a+b)^{2005}}{(c+d)^{2005}}\)

f, \(\dfrac{(a^{2004}+b^{2004})^{2005}}{(c^{2004}+d^{2004})^{2005}}\) = \(\dfrac{(a^{2005} -b^{2005})^{2004}}{(c^{2005}-d^{2005})^{2004}}\)