Question

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

cm a/2=b/3

Answer 1

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

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

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

\(\Rightarrow4b=6a\)

\(\Rightarrow\frac{a}{b}=\frac{4}{6}=\frac{2}{3}\Rightarrow3a=2b\Rightarrow\frac{a}{2}=\frac{b}{3}\)

Đpcm

 

 

 

Answer 2

Ta có:\(\frac{a+2}{a-2}\)=\(\frac{b+3}{b-3}\)

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

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

Ta có:\(\frac{a+2}{b+3}\)=\(\frac{a}{b}\)

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

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

\(\Rightarrow2b=3a\)

\(\Rightarrow\)\(\frac{a}{2}=\frac{b}{3}\)(đpcm)