CHAPTER XV.
Fractional and Literal Equations.
163. In this chapter we propose to give a miscellaneous collection of equations. Some of these will serve as a useful exercise for revision of the methods already explained in previous chapters; but we also add others presenting more difficulty, the solution of which will often be facilitated by some special artifice.
The following examples worked in full will sufficiently illustrate the most useful methods.
Ex. 1. Solve 4 - {x - 9}{8} = {x }{ 22} -{1} {2}
Multiply by 88, which is the least common multiple of the denomi- nators, and we get 352- 11(x-9)=4x-44; removing brackets, 352 — 11x + 99 = 4x — 44; transposing, — 11x — 4x= — 44 — 352 — 99 ; collecting terms and changing signs, 15 x= 495 ; x = 33.
Note. In this equation - {x - 9}{8} is regarded as a single term with the minus sign before it. In fact it is equivalent to — {1}{8} (x — 9), the line between the numerator and denominator having the same effect as a bracket.
Ex.2. Solve {8x+23}{20} - {5x+2} {3x + 4} ={2x+3}{ 5 }
Multiply by 20, and we have 8x + 23 - {20(5x+2)} {3x + 4} = 8x + 12 - 20. By transposition, 31 = {20(5x + 2)}{3x + 4}
