Question

CHO PHÂN SỐ \(\frac{a}{b}\)khác 1

tìm phân số \(\frac{c}{d}\)sao cho \(\frac{a}{b}+\frac{c}{d}=\frac{a}{b}.\frac{c}{d}\)

Answer 1

\(\frac{a}{b}+\frac{c}{d}=\frac{a.c}{b.d}\)

Vậy \(\frac{a.d+b.c}{bd}=\frac{ac}{bd}\)

\(\Leftrightarrow ad+bc=ac\)

\(\Leftrightarrow ad=ac-bc\)

\(\Leftrightarrow ad=c\left(a-b\right)\)

\(\Leftrightarrow\frac{a}{b}=\frac{a}{a-b}\)

Answer 2

\(\frac{a}{b}+\frac{c}{d}=\frac{a\cdot c}{b\cdot d}\)

Vậy \(\frac{a\cdot b+b\cdot c}{bd}=\frac{ac}{bd}\)

\(\Rightarrow ad+bc=ac\)

\(\Rightarrow ad=ac-bc\)

\(\Rightarrow ad=c\left(a-b\right)\)

\(\Rightarrow\frac{a}{b}=\frac{a}{a-b}\)