2p4 iXGEBRJ:* 



5. Thus; a^lfX-^-acx^-^ax^ divided by adX'^afi:^ 



a*bx4-acx ' -A-aX ^ ab-^-cX-A-X * 



gives p-, > or — ---— ' . 



^ adX-^-anx d-{-n 



, . a^hx-i^cX^-^-aX^ . 



Here the quotient —-,- — = • is reduced to 



, adx-YanX 



ah'\-cx-\-x'' ,,..,. 



■ ^ ; • > by dividing e^^ery term of its numerator a^d 



denominator by ax, 



6. And a-^-ab'^d^ divided by « ' -— ^^-J-^ * ^ * gives 



Here the quotient cannot be reduced to lower terms, be- 

 cause the factor a is not to be found in the term d^ . 



But it is to^be observed, tlwt though a fraction cannot 

 be reduced to lower terms by a simple divisor, yet it may 

 sometimes be so reduced by a compound one j as Vviill ap- 

 pear in the reduction of fractions. 



^ 7. Divide c^-j-^^ by ^z+a:. Ans. «*— ^ft:-}-;c*. 



8. Divide a? — 3«*}'"[-3^j'* — y"^^ by a — y* 



Ans. a^ — 2^>'-f7*' 



9. Divide 6;!^^ — -96 by 3A?— 6. 



Ans. 2a;^+4a?'4"^''^4"^^' 



10. Divide a^ — -^a^X-^lOa^^x'^ — 10^ 'a; ^+5'^^'^'^ — ^^ ^7 

 c*— 2^^:-}-;;*. Ans. a}"^l^a^ x-\-y*^^ "^^^^ 



FRACTIONS. 



Algebraic Fractions. have the same names and rules 

 of operation, as fractions in Arithmetic. 



PROBLEH 



