SOLUTIONS TO THE EXERCISES.] M ATHE M ATICS. ALGEBR A. 407 



. ; Otherwise, 



a-b 



a-4 



DIVISION OP FRACTIONS. EXAMPLES FOB EXERCISE. PAGE 4G9. 



_._ jr' + 2 _ x 3 + 2x 2 g + 1 x g _ _J 



_ 2 * I ~ x* 3x + 2 a a- 1 a 1 



S. 1 ^--:- 2 ^ = ?L 5 -r T = 1 -5 X4 = ^ . fc 4 _ , *- FJTJ ~ * ~ * to -^ 



6 



' 



SIMPLE EQUATIONS IN GENERAL. EXAMPLES IN EQUATIONS WITH ONLY ONE UNKNOWN QUANTITY. PAGE 470. 

 1. ~ + ~ = 22 +-?- Multiplying the terms of tho second fraction by 3, 



y + -Q =22 +-Q- 



2x x 

 Transposing, -g- + 3 =22. 



Clearing, 6* + 5x = 330, that is, llx = 330 /. x = 30. 



This might also have been readily solved by multiplying each side of tho proposed equation by 30, tho least 

 number divisible by all tho denominators ; the equation thus cleared of fractious would have been 



12x + 15* = CCO + 5 

 .-. 27x 6x = 660, /. 22* = GOO, /. x = 30. 



2. 'L + -^ + ~ = c.J. Multiplying by 12, the least common multiple of tho denominators, we have 



that is, 13* = 78, .'. x = 6. 



x x 

 Multiplying by 12, 3x = 2x + 12, . . x = 12. 



ix.'.x = 3. 



5 . 21+ 3^^ = 5(x_-l) + 97^r < Multiplyingbyl6j 



336 + Zx 11 =. 10* 10 + 776 56*. 

 Transposing, 66* + 3* lOx = 770 + 11 10 336 

 . . 49x = 441, . . x = 9. 



Squaring, x 2 + 7 = 49 14* + x 1 , . . 14* = 42, . . x = 3. 



7. v/(* ) 6=0,.'. J(x a) = 6, .'. x a = 6 2 , .-.x = a+6 2 . 



t ' | rt O ^ 35 5 I -\ r\ 1 Ai 



8. ^^o = 2' A PP lvin 8 the pri nci P le explained at page 468, we have -^ = J > ' V * = 10 > " * * 



28 = VfHl??. Applying the principle referred to in tho last example, we havo 



?x = *^~fjr~~' Multiplying by 3.4.4, 

 4 v /* + 64 = 3 v /x + (W, .-. v /x=2,.-.x = 4. 



,v rz ^ za V* + * a T. n --i ^ra 



10. y , r -h -5-,- By tho principle at page 408, 



zyx-r-za-t-o = 1V_* - ; that is 



2 6 4a 36 



2 ^x , 2a + 6 a 2 Vx ^.4a+j6 

 2a ^F 2o 6 4a 36 4a 36 



2 ijx 2 V x 4a + 3b 2a + 6 

 Transposing, 2^T&~ 40^36" 4a 36 ~2a 6* 



Multiplying by (2a 6) (4a 36), 



8a Vx-66 V-4a Vx + 26 ^x = (2a-6) (4a + 36)-(2a + 6) (4a- 36) 

 .-. (4a 46) v'x - 8a6 + 12o6 = 4a6, 



a6 / a6 ^ 



.'. Jx=- ri I .x I- r) 



v.ii.. r. 



