Vì\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)

Đặt \(\frac{a}{c}=\frac{b}{d}\) = k

=> a = ck , b = dk

Thay a = ck , b = dk vào  \(\frac{7a-11b}{4a+5b}\)ta có :

\(\frac{7a-11b}{4a+5b}=\frac{7.ck-11dk}{4ck+5dk}=\frac{k\left(7c-11d\right)}{k\left(4c+5d\right)}=\frac{7c-11d}{4c+5d}\)

Vậy \(\frac{7a-11b}{4a+5b}=\frac{7c-11d}{4c+5d}\)

đúng rồi

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

=>\(a=bk;c=dk\)

1: \(\dfrac{2a+3c}{2b+3d}=\dfrac{2\cdot bk+3\cdot dk}{2b+3d}=\dfrac{k\left(2b+3d\right)}{2b+3d}=k\)

\(\dfrac{2a-3c}{2b-3d}=\dfrac{2bk-3dk}{2b-3d}=\dfrac{k\left(2b-3d\right)}{2b-3d}=k\)

Do đó: \(\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)

2: \(\dfrac{4a-3b}{4c-3d}=\dfrac{4\cdot bk-3b}{4\cdot dk-3d}=\dfrac{b\left(4k-3\right)}{d\left(4k-3\right)}=\dfrac{b}{d}\)

\(\dfrac{4a+3b}{4c+3d}=\dfrac{4bk+3b}{4dk+3d}=\dfrac{b\left(4k+3\right)}{d\left(4k+3\right)}=\dfrac{b}{d}\)

Do đó: \(\dfrac{4a-3b}{4c-3d}=\dfrac{4a+3b}{4c+3d}\)

3: \(\dfrac{3a+5b}{3a-5b}=\dfrac{3bk+5b}{3bk-5b}=\dfrac{b\left(3k+5\right)}{b\left(3k-5\right)}=\dfrac{3k+5}{3k-5}\)

\(\dfrac{3c+5d}{3c-5d}=\dfrac{3dk+5d}{3dk-5d}=\dfrac{d\left(3k+5\right)}{d\left(3k-5\right)}=\dfrac{3k+5}{3k-5}\)

Do đó: \(\dfrac{3a+5b}{3a-5b}=\dfrac{3c+5d}{3c-5d}\)

4: \(\dfrac{3a-7b}{b}=\dfrac{3bk-7b}{b}=\dfrac{b\left(3k-7\right)}{b}=3k-7\)

\(\dfrac{3c-7d}{d}=\dfrac{3dk-7d}{d}=\dfrac{d\left(3k-7\right)}{d}=3k-7\)

Do đó: \(\dfrac{3a-7b}{b}=\dfrac{3c-7d}{d}\)

\(\frac{a}{b}=\frac{c}{d}\)

\(\left(2a+3b\right)\left(4c-5d\right)=\left(4a-5b\right)\left(2c+3d\right)\)

\(\Leftrightarrow8ac-10ad+12bc-15bd=8ac+12ad-10bc-15bd\)

\(\Leftrightarrow-10ad+12bc=12ad-10bc\)

\(\Leftrightarrow\left(-10ad+12bc\right)+\left(-12bc-12ad\right)=\left(12ad-10bc\right)+\left(-12bc-12ad\right)\)

\(\Leftrightarrow22bc=22ad\)

vì a/b=c/d nên => a/c=b/d

đặt a/c=b/d =k thì => a=ck ; b= dk 

thay a=ck và b=dk vào 2a-3b/4a+5b có 

\(\frac{2a-3b}{4a+5b}=\frac{2ck-3dk}{4ck+5dk}=\frac{k\left(2c-3d\right)}{k\left(4c+5d\right)}=\frac{2c-3d}{4c+5d}\)

từ đay suy ra 2a-3b/4a+5b=2c-3d/4c+5d 

a/b=c/d <=>a/c=b/d

=>4a/4c=5b/5d

Áp dụng.. ta có:

4a/4c=5b/5d=4a-5b/4c-5d=4a+5b/4c+5d

=>4a-5b/4a+5b=4c-5d/4c+5d(đpcm)

 Tick nhé

chtt ! tick minh nha ban

Vì : a/b=c/d nên =>a/c=b/d

Đặt: a/c=b/d=k thì =>a=ck;b=dk

Thay :a=ck và b=dk vào 2a-3b/4a+5b có : 

2a-3b/4a+5b=2ck-3dk/4ck+5dk=k(2c-3d)/k(4c+5d)=2c-3d/4c+5d

Tu đây suy ra : 2a-3b/4a+5b=2c-3d/4c+5d

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