50 AUiE^BRA. 



31. ExAMPLKvS. We append a few miscellaneous examples on 

 the last two chapters. 



JL x i 

 7. Does (a-\-x)'^=a'^+x'^ f 



2. Multiply together >/a , 'V b\ </ r , ^3^?"^ and cT'^ . 



2 2 



T^H^yr y — x" 



J. Simplify -3-_:7,r X T - 1 



4. Multiply together 



\^x^'"+x"y^y", s^x"—y\ \/ x'" —x"y" -\-y'" and s/ x" -^-y". 



5. Multiply together 



1 i 1 I 



(a'-^ab-^-b')-, (a—b)-, (a—b)'- and (d'-\-ab + b')- 



d^ — x^ 



a — X 



6. Simplify "/""/-' -J 



-^"^ +1 



Va—x 



^. ..r x-i-x^x'—y .r'-' . 



7. Simplify y^^, 2 ~^,-hi 



x—'^x^—y y~ 



^. Cube the expression a^s/x—\^baVy, 



g. Prove 2 + ^3 is the reciprocal of 2— ^3 ; and find what 

 must be the relation between the two terms -r and v^j/ so that 

 x-\-s/ y shall be the reciprocal of .r— v/j. 



TO. Simplyfy I — 



I (x^-a)' 



(i^xf-\(\-xf 

 1 I 



jr. SimpHfy the expression 



(Y^x)-'-(i-xr 



first by rationalizing the numerator, and then by rationalizing 

 the denominator. 



12. Prove that if /=3 and ^7=5, 



e'-'^-pq-"" -^qp'^ - f ^^~^^ 3^^' + 5 



pq - ' e^''-V2-^qp-^c'^-' 3 + 5^'' 



