CMR : nếu \(\frac{a}{b}=\frac{c}{d}\) thì :
a) \(\frac{5a+3b}{5a-3b}-\frac{5c+3b}{5c-3d}\)
b) \(\frac{7a^2+3ab}{11a^2-8b^2}=\frac{7c^2+3cd}{11c^2-8d^2}\)
b, Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=b.k,c=d.k\)
+) \(\frac{7a^2+3ab}{11a^2-8ab^2}=\frac{7k^2.b^2+3kb^2}{11k^2.b^2-8b^2}=\frac{7k^2+3k}{11k^2-8}\left(1\right)\)
+) \(\frac{7c^2+3cd}{11c^2-8d^2}=\frac{7k^2.d^2+3k.d^2}{11k^2.d^2-8d^2}=\frac{7k^2+3k}{11k^2-8}\left(2\right)\)
Từ (1) và (2) => ĐPCM
1. Cho: \(\frac{a}{b}\)= \(\frac{c}{d}\). C/m : a) \(\frac{10a-b}{3a+7b}\)= \(\frac{10c-d}{3c+7d}\)
b) \(\frac{7a^2+3ab}{11a^2-8b^2}\)= \(\frac{7c^2+3cd}{11c^2-8d^2}\)
2. Cho : \(\frac{a}{b}\)=\(\frac{b}{c}\)=\(\frac{c}{d}\). C/m : \(\left(\frac{a+b+c}{b+c+d}\right)^3\)= \(\frac{a}{d}\)
CMR nếu \(\frac{a}{b}=\frac{c}{d}\) thì: \(\frac{9a^2+3ab}{11a^2+7b^2}=\frac{9c^2+3cd}{11c^2+7d^2}\)
cho tỉ lệ thức a/b = b/c
cmr : \(\frac{3ab}{3cd}=\frac{2a^2-3b^2}{2c^2-3d^2}\)
bài giải nhé
cho \(\frac{a}{b}=\frac{c}{d}\)
CMR ta có tỉ lệ thức \(\frac{a^2+b^2}{c^2+d^2}=\frac{ad}{cd}\)
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\), chứng minh rằng
\(\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)
Cho tỉ lẹ thức \(\frac{a}{b}=\frac{c}{d}\)Chứng minh rằng \(\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\).
Cho \(\frac{a}{b}=\frac{c}{d}.CMR\frac{a^2+b^2}{b^2+c^2}=\frac{a}{c}\)