a) Cho hai phân số a/b và a/c có a=b+c (a,b,c thuộc Z, b khác 0, c khác 0)

* Hướng dẫn giải

a)

$\left.\begin{array}{c}\frac{a}{b}\text{ . }\frac{a}{c}=\frac{a^2}{bc}\\ \\ \frac{a}{b}\text{ + }\frac{a}{c}=\frac{ac+ab}{bc}=\frac{a(b+c)}{bc}=\frac{a^2}{bc}\end{array}\right\}\Rightarrow \frac{a}{b}\text{ . }\frac{a}{c}\text{ = }\frac{a}{b}\text{ + }\frac{a}{c}$

b)

$\begin{array}{l}a=12;b=-5\Rightarrow \text{ c = 17}\\ \left.\begin{array}{c}\frac{12}{-5}.\frac{12}{17}=\frac{-144}{85}\\ \\ \frac{12}{-5}+\frac{12}{17}=\frac{-204}{85}+\frac{60}{85}=\frac{-144}{85}\end{array}\right\}\Rightarrow \frac{12}{-5}.\frac{12}{17}=\frac{12}{-5}+\frac{12}{17}\end{array}$