According to it,

$text\{if\; \}\; frac\{a\}\{b\}\; =\; frac\{c\}\{d\}\; text\{\; then\; \}\; frac\{a+b\}\{a-b\}\; =\; frac\{c+d\}\{c-d\}.$

Proof

Add one to both sides of the equality a / b = c / d to get

$frac\{a\}\{b\}\; +\; 1\; =\; frac\{c\}\{d\}\; +\; 1\; implies\; frac\{a+b\}\{b\}\; =\; frac\{c+d\}\{d\}.\; qquad\; (1)$

$frac\{a\}\{b\}\; -\; 1\; =\; frac\{c\}\{d\}\; -\; 1\; implies\; frac\{a-b\}\{b\}\; =\; frac\{c-d\}\{d\}.\; qquad\; (2)$