Question

Chứng minh rằng:

Nếu: \(c+b=a\) thì \(\frac{a}{b}.\frac{a}{c}=\frac{a}{b}+\frac{a}{c}\)

Answer 1

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

Xét Hiệu : \(\frac{a}{b}.\frac{a}{c}-\left(\frac{a}{b}+\frac{a}{c}\right)\)

\(=\frac{a^2}{bc}-\frac{ac+ab}{bc}\)

\(=\frac{a^2}{bc}-\frac{a\left(c+b\right)}{bc}\)

\(=\frac{a^2}{bc}-\frac{a^2}{bc}\)  \(\left(c+b=a\right)\)

\(=0\)

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

Answer 2

Ta có:

\(VT=\frac{a}{b}.\frac{a}{c}=\frac{aa}{bc}=\frac{a^2}{bc}\)

\(VP=\frac{a}{b}+\frac{a}{c}=\frac{ac}{bc}+\frac{ab}{bc}=\frac{a\left(c+b\right)}{bc}=\frac{aa}{bc}=\frac{a^2}{bc}\)

\(\Rightarrow VT=VP\)

Vậy nếu \(c+b=a\) thì \(\frac{a}{b}.\frac{a}{c}=\frac{a}{b}+\frac{a}{c}\) (Đpcm)