^4 Algebra. 



Sometimes such equations are best simplified by first rationaliz- 

 ing either the numerator or denominator of the fraction. Ration- 

 alizing the denominator of this fraction, the equation becomes 

 2x-{-a-\-2\/ ax-i-x'^__ 

 X — a — X ' 



or 2s/ ax-\-x^=^ — (ax-\-2x-\-a), 



whence ^.ax -\- ^x^ = ( ax -\- 2x-\-a)\ 



etc. 

 SoU^e -t-f- \/ X -|- 3=4-*' — I . 



Solve ^'14 — x-\- s/ II — x= ^ r-— 



V II — ^ 



Solve s/ ^x 4- 9— V-t" — i=s/ X -f 6. 



Solve V-^ — 9+ V-^ + i2= V-^ — 4+ V-^4- 13. 



Solve sf x^a" — ^ x=b. 



Solve -__ — V iO->t"— 9= -j-Q. 



Viojr — 9 Viojr — 9 



vSolve V6.r-f4 + >/^^-f i^4-~3F-fio=-^H-3- 



vSolve ' ^ 2 V 4X - y ^ 3 - 4 V 4 ~ji: -7 



6 4-5>/4-^' — 7 3— io\/4-^— 7 



Solve , - r -'—__ — = I . 



<^\^-x'—^\—x' 



Rationalize ^ x^— sf x^=o. 

 Solve ^^+^^-3_ 3 



II 



J2 



^ 3c— \/ X — 3 -^~3- 

 Criticise the following solution : 



Multiply both terms of the first fraction by f*J x-\- sj x—'^, and 

 we have 



{sl'x-]r \^'x-^\' _ 3 /,x 



or . ,. , (V-^+ V-^'— 3)'= 7^ • r3/> 



X 3 



Kxtracting the square root, 



sj x^s/ x~i= ^ • (^) 



\/ x—\ 



