DIVISION. 293 



4. Divide «^ — 3«'-^4-4«<:*— #^*"by a'— 2^1:+^ . 



.» /.I 



ac — c 



^ * ^2^^+c * )« ' -r 3^ ' ^+4^^ ' — 2<r * (a—r+jr^J^^q::; 



— a*C'\'2ac'' — c^ 

 Remains + ac"" — * c^ 



Here it is obvious, tKat the division cannot terminate 

 v^^ithout a remainder •, therefore we virrite the divisor under 

 the remainder with a line between them, and add the 

 fraction to a — r, the other two terms, to complete the 

 quotient. 



But when the dividend dees not precisely contain the 



divisor, then we generally express the whole quotient as a 



fraction, having reduced it to its lowest terms, or rejected 



the letters and factors, that are found in every term of the 



'i^iS'^ividend and divisor. 



5. Thus, 



that corresponds to — j/ab , the second term of this product, 

 we subtract a — ^/ab from a — 5, the dividend, and the sign of 

 the quantity — //ab being changed, the remainder is •\'//ab — b» 

 l\o\v -j- \/ab , the first term of this remainder, divided by \/a , 



the first term of the divisor, gives — \/b for- the second term 

 of the quotient, by which we multiply the divisor, and the prod- 

 uct, viz. -{-^ab — b, being subtracted from the aforesaid re« 

 cjainder, nothing remains ; and the quotient is j/a-i^^/h. 



