Question

chứng minh rầng a+2/a-2=b+3/b-3 thì a/2=b/3

Answer 1

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

=> ( a+ 2 )(b - 3 ) = ( b + 3  )(a - 2 )

=> ab  - 3a + 2b - 6 = ab - 2b + 3a -6 

=> ab - 3a + 2b - 6 - ab + 2b - 3a + 6 = 0 

=> 4b - 6a = 0 

=> 4b = 6a

=> 2.2b = 2.3a

=> 2b = 3a

=> b/3 = a/2  

Answer 2

\(\frac{a+2}{a-2}=\frac{b+3}{b-3}\Leftrightarrow\left(a+2\right)\left(b-3\right)=\left(a-2\right)\left(b+3\right)\Leftrightarrow3a=2b\Leftrightarrow\frac{a}{2}=\frac{b}{3}\)

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