Additional Formulas: a/b - (na-1)/(nb-1)

This is a supplement to the formulas in Section 1.5.5, dealing with specific forms of fraction subtraction. There are four variations in total, which are useful for quickly solving otherwise tedious problems.

Formulas:

• $\frac{a}{b} - \frac{na-1}{nb-1} = \frac{b-a}{b(nb-1)}$
• $\frac{a}{b} - \frac{na+1}{nb+1} = -\frac{b-a}{b(nb+1)}$

The key is to observe the numerator and denominator of the more complex fraction to see if they are one greater or one fewer than a multiple of the simpler fraction's numerator and denominator. This determines which formula to apply.