When x is added to both the numerator and the denominator of the fraction a/b, where a and b are both not equal to 0, the value of the fraction is changed to c/d. Then what is x?
| a + x | = | c |
| b + x | d |
→ d(a + x) = c(b + x)
→ ad + dx = bc + cx
→ dx – cx = bc – ad
→ x(d – c) = bc – ad
→ ad + dx = bc + cx
→ dx – cx = bc – ad
→ x(d – c) = bc – ad
| → x = | bc – ad | = | ad – bc |
| d – c | c – d |