\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{2a}{2c}=\frac{5b}{5d}=\frac{2a-5b}{2c-5d}\)

mà \(\frac{a}{c}=\frac{3a}{3c}\)

\(\Rightarrow\frac{2a-5b}{2c-5d}=\frac{3a}{3c}\Rightarrow\frac{2a-5b}{3a}=\frac{2c-5d}{3c}\)

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

\(\Rightarrow\frac{2a}{2c}=\frac{5b}{5d}=\frac{2a-5b}{2c-5d}\)

Mà \(\frac{a}{c}=\frac{3a}{3c}\Rightarrow\frac{2a-5b}{2c-5d}=\frac{3a}{3c}\Rightarrow\frac{2a-5b}{3a}=\frac{2c-5d}{3c}\)

(ĐPCM)

MK LÀ NGƯỜI TRẢ LỜI ĐẦU TIÊN NHA MẤT MÔT HỒI MỚI NGHĨ RA

Đặt a/b=c/d=k

=>a=bk; c=dk

\(\dfrac{2a+b}{3a-5b}=\dfrac{2\cdot bk+b}{3\cdot bk-5b}=\dfrac{2k+1}{3k-5}\)

\(\dfrac{2c+d}{3c-5d}=\dfrac{2dk+d}{3dk-5d}=\dfrac{2k+1}{3k-5}\)

Do đó: \(\dfrac{2a+b}{3a-5b}=\dfrac{2c+d}{3c-5d}\)

Cách khác:

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\left\{{}\begin{matrix}\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{2a+b}{2c+d}\\\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{3a-5b}{3c-5d}\end{matrix}\right.\)

\(\Rightarrow\dfrac{2a+b}{2c+d}=\dfrac{3a-5b}{3c-5d}\Rightarrow\dfrac{2a+b}{3a-5b}=\dfrac{2c+d}{3c-5d}\left(đpcm\right)\)

Đặt \(\frac{a}{b}=\frac{c}{d}=k=>a=bk;c=dk\)

Khi đó : \(\frac{2a+5b}{3a-4b}=\frac{2bk+5b}{3bk-4}=\frac{b\left(2k+5\right)}{b\left(3k-4\right)}=\frac{2k+5}{3k-4}\)

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

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

MK LÀM NHƯ VẬY K BÍT CÓ Đ K , BẠN YÊU à!!!!!!!!!!!!!!!!

Ta có : \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{2a}{2c}=\frac{5b}{5d}=\frac{3a}{3c}=\frac{4b}{4d}=\frac{2a+5b}{2c+5d}=\frac{3a-4b}{3c-4d}\)

Suy ra : \(\frac{2a+5b}{3c-4d}=\frac{2c+5d}{3a-4b}\) (đpcm)

Bạn xem lại đề bài

Hai mẫu số giống nhau à

\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{2a}{2c}=\frac{5b}{5d}=\frac{2a-5b}{2c-5d}\)

\(\Rightarrow\frac{a}{c}=\frac{3a}{3c}=\frac{2a-5b}{2c-5d}\Rightarrow\frac{2a-5b}{3a}=\frac{2c-5d}{3c}\left(dpcm\right)\)

Giải:

Ta có: \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\frac{a}{c}=\frac{b}{d}=\frac{2a}{2c}=\frac{5b}{5d}=\frac{2a+5b}{2c+5d}\)

\(\frac{a}{c}=\frac{b}{d}=\frac{3a}{3c}=\frac{4b}{4d}=\frac{3a-4b}{3c-4d}\)

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

\(\Rightarrow\frac{2a+5b}{3a-4b}=\frac{2c+5d}{3c-4d}\left(đpcm\right)\)

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