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

\(\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2b^2k^2-3b^2k+5b^2}{2b^2+3b^2k}=\frac{b^2\left(2k^2-3k+5\right)}{b^2\left(2+3k\right)}=\frac{2k^2-3k+5}{3k+2}\)

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

nên 2 phân số trên bằng nhau (đpcm)

Đặt: \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)

Ta có : \(\frac{2a^2-3ab+5b^2}{2b^2+3ab}\)

<=> \(\frac{2b^2k^2-3b^2k+5b^2}{2b^2+3b^2k}\)

<=> \(\frac{b^2\left(2k^2-3k+5\right)}{b^2\left(2+3k\right)}\)

<=> \(\frac{2k^2-3k+5}{2+3k}\left(1\right)\)

Ta có: \(\frac{2c^2-3cd+5d^2}{2d^2+3cd}\)

<=> \(\frac{2d^2k^2-3d^2k+5d^2}{2d^2+3d^2k}\)

<=> \(\frac{d^2\left(2k^2-3k+5\right)}{d^2\left(2+3k\right)}\)

<=> \(\frac{2k^2-3k+5}{2+3k}\left(2\right)\)

Từ 1 và 2 => đpcm

Điều kiện mẫu thức xác định là sao?

Mình hướng dẫn thôi. Chứ giờ đang bận.

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=kb\\c=kd\end{cases}}\).Rồi thay a = kb; c=kd vào từng vế. Thấy hai vế bằng nhau => đpcm

\(\frac{a}{b}=\frac{c}{d}=>\frac{a}{c}=\frac{b}{d}=>\frac{2a^2}{2c^2}=\frac{5b^2}{5d^2}=\frac{3ab}{3ab}=\frac{3cd}{3cd}\)

áp dụng t/c dãy tỉ số bằng nhau ta có:

\(\frac{2a^2}{2c^2}=\frac{5b^2}{5d^2}=\frac{3ab}{3ab}=\frac{3cd}{3cd}=\frac{2a^2-3ab+5b^2}{2b^2-3cd+5d^2}=\frac{2b^2+3ab}{2d^2+3cd}\)

\(=>\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2c^2-3cd+5d^2}{2d^2+3cd}\)

Đặt a/b=c/d=k rồi thay vào nha bạn

GỢI Ý:

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

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

\(\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2\left(bk^2\right)-3bkb+5b^2}{2b^2+3bkb}=\frac{2b^2.k^2-3kb^2+5b^2}{2b^2+3b^2.k}\)\(=\frac{b^2\left(2k^2-3k+5\right)}{b^2\left(2+3k\right)}=\frac{2k^2-3k+5}{2+3k}=\frac{2c^2-3cd+5d^2}{2d^2+3cd}\)\(=\frac{2\left(dk\right)^2-3dkd+5d^2}{2d^2+3dkd}=\frac{2d^2k^2-3d^2k+5d^2}{2d^2+3dkd}\)

Tương tự nhóm tiếp là ra

=>bằng nhau

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Leftrightarrow a=bk,c=dk\)

Thay a = bk, c = dk vào \(\frac{7a^2+3ab}{2a^2-ab}\)và \(\frac{7c^2+3cd}{2c^2-cd}\), ta có:

\(\frac{7a^2+3ab}{2a^2-ab}=\frac{7\left(bk\right)^2+3.bk.b}{2\left(bk\right)^2-bk.b}=\frac{7b^2k^2+3b^2k}{2b^2k^2-b^2k}=\frac{b^2k\left(7k+3\right)}{b^2k\left(2k-1\right)}=\frac{7k+3}{2k-1}\)

\(\frac{7c^2+3cd}{2c^2-cd}=\frac{7\left(dk\right)^2+3.dk.d}{2\left(dk\right)^2-dk.d}=\frac{7d^2k^2+3d^2k}{2d^2k^2-d^2k}=\frac{d^2k\left(7k+3\right)}{d^2k\left(2k-1\right)}=\frac{7k+3}{2k-1}\)

\(\Rightarrow\frac{7a^2+3ab}{2a^2-ab}=\frac{7c^2+3cd}{2c^2-cd}\left(đpcm\right)\)

Đặt a/b=c/d=k thì a=bk, c=dk

*7a^2 ₊3ab/2a²-ab=7b²k²+3b²k/2b²k²-b²k=b²k(7k+3)/b²k(2k-1)=7k+3/2k-1  (1)

Tương tự 7c²+3cd/2c²-cd=7k+3/2k-1  (2)

từ (1) và (2) suy ra :

7a²+3ab2a²−ab =7c²+3cd2c²−cd