MATHEMATICS. ALGEBRA. [SOLUTIONS TO THE EXEBCUHL 



8 [<* + jr) + f ] [(* + jr) n] _ S - 





f 



- . (x y)-* _ (x-y-z) (x 



10 x'-Sx- - _ 



- 3 ) (*-2)-3(3-x)} _ 



_ 



x {(x 3)(x 2) + 3(x 3)} _ x(x 3)(x 2 + 3) _x(x 3)(x 

 x 2 * 2 x 2 



g (s ax 3) _ x(x 2x+l 4) x j(x 1)' 4J 

 * 2 * 2 x 2 



ADDITION AND SUBTRACTION or FRACTIONS. EXAMPLES FOR EXEBCISB. PAGE 4C3. 



2x 5 , x 1 4x 10x + 3x 3 4j;' 7x 3 

 L ~~~ ~"' ~~ ~~ 



__*_ g 





___ 



x 3 x + 3 3? 9 x* 9' 



IPs 9_3x 5 70x 63 24x + 40 46x 23 



8 7 . r 'i . r ,ii 



3_x 5 16x* 24x 7x + 35x 9x > +ll!g_ Ox 



7x 8x 66x 66x 5 



x a 4. 1 _, x 8 a' + x* og +Q 1 = 2x' ox 

 x' ox + a' " t "x+~q = x s + o ~ " ' 



_ JT a_x + q x + q_ 2a _ = 



_ 



x + o x + o x + a xy yz xyz 



In this seventh example, tlio terms of the first fraction are multiplied by z, and those of the second by x ; the 

 ili'iioiiiiiiutors thus become each equal to xyz. 



8. '^+^11 ~- Multiplying the terms of the first fraction by j ', and those of the second by t" ', we hare 



* a' 



i _ 



~" 



* 



, 2 JL __ 







__ _ __ 



y-3 y "f'y + S y 



0-. ..I I 3y L .,? _ Jy 2l/* 



The second and fourth fractions united give -- * =: 2, the first and third make "5ig" i^To' Heucc tllc 



_. 



14 _*_ y _ry+***yy* __ ^ 



~ ~ 



. 

 y + z 



MULTIPLICATION OF FRACTIONS. EXAMPLES FOB EXEBCISB. PAGE 4C>!>. 

 5 * 5 * 



- - - - 2 - r -- 



7 9* 7 9 63x " 3"^ T ' 1 ~ 7 



8 1+-* X _,*!fL - 1 v ** - ** **- * - 



x _4- X ^*-^T- 6 - ji X ^j^ - ^j^ 



7 *" x *"-*"*' 8 - v^- 



' y A y y-+- " y . x , iyta- 



Iii tliiii tenth example it b seen at once that the numerator of the second fraction is divisible by the denominator 

 f tlio first, because if q be put for z in x 3 o', the result is 0.* 



11 ^ v 4l v 7 v 9J: - l, v l v * - 2 ** 

 "XXX--a Ks:-, 



14 (j ~' : v* + y_ *~y v fr i ^ ___ *~ y 



' ^'-y' X *-y-(;c'-y')(4-'+y')* ~ (, - y) (p* 



Sc p. 493. . - 



