Question

chứng minh rằng \(\frac{a}{b}\)=\(\frac{c}{d}\)thì \(\frac{a}{b}\)=\(\frac{a+c}{b+d}\)=\(\frac{a-c}{b-d}\)

Answer 1

a/b=c/d<=> ad=bc

a/b= (a+c)/(b+d) <=> a(b+d)=b(a+c) <=> ab+ad=ab+bc <=> ad=bc(đúng) 

a/b= (a-c)/(b-d) <=> a(b-d)=b(a-c) <=> ab-ad=ab-bc <=> ad=bc(đúng) 

=> đpcm

Answer 2

Goi a/b=c/d=k

=>a=bk va c=dk

a+c/b+d=bk+dk/b+d=k(b+d)/b+d=k

=>a/b=c/d=>a/b=a+c/b+d 

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