Question

[Nguyễn Anh Thư]

bài 3

Cho \(\dfrac{a+2}{a-2}=\dfrac{b+3}{b-3}\) Chứng minh \(\dfrac{a}{2}=\dfrac{b}{3}\)

giúp mk với

Answer 1

[Mysterious Person]

ta có : \(\dfrac{a+2}{a-2}=\dfrac{b+3}{b-3}\Leftrightarrow\left(a+2\right)\left(b-3\right)=\left(b+3\right)\left(a-2\right)\)

\(\Leftrightarrow ab-3a+2b-6=ab-2b+3a-6\Leftrightarrow-3a+2b=-2b+3a\)

\(\Leftrightarrow2b+2b=3a+3a\Leftrightarrow4b=6a\Leftrightarrow2b=3a\Leftrightarrow\dfrac{a}{2}=\dfrac{b}{3}\left(đpcm\right)\)

Answer 2

[Mashiro Shiina]

\(\dfrac{a+2}{a-2}=\dfrac{b+3}{b-3}\)

\(\Rightarrow\left(a+2\right)\left(b-3\right)=\left(a-2\right)\left(b+3\right)\)

\(\Rightarrow a\left(b-3\right)+2\left(b-3\right)=a\left(b+3\right)-2\left(b+3\right)\)

\(\Rightarrow ab-3a+2b-6=ab+3a-2b-6\)

\(\Rightarrow ab-3a+2b=ab+3a-2b\)

\(\Rightarrow ab-3a+4b=ab+3a\)

\(\Rightarrow ab+4b=ab+6a\)

\(\Rightarrow4b=6a\)

\(\Rightarrow\dfrac{a}{4}=\dfrac{b}{6}\)

\(\Rightarrow\dfrac{a}{2}=\dfrac{b}{3}\rightarrowđpcm\)