Question

Cmr nếu a+2/a-2=b+3/b-3 thì a/2=b/3

Answer 1

\(\dfrac{a+2}{a-2}=\dfrac{b+3}{b-3}\\ \Leftrightarrow\dfrac{a+2}{b+3}=\dfrac{a-2}{b-3}=\dfrac{a+2+a-2}{b+3+b-3}=\dfrac{2a}{2b}=\dfrac{a}{b}\\ \dfrac{a+2}{b+3}=\dfrac{a-2}{b-3}=\dfrac{4}{6}=\dfrac{2}{3}\\ \Rightarrow\dfrac{a}{b}=\dfrac{2}{3}\)

Answer 2

Ta có:

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

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

\(\Rightarrow\dfrac{a+2}{b+3}=\dfrac{a-2}{b-3}=\dfrac{a}{b}=\dfrac{4}{6}=\dfrac{2}{3}.\)

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

\(\Rightarrow\dfrac{a}{2}=\dfrac{b}{3}\left(đpcm\right).\)