AlgMap-4.13 Express {@p@} as a single fraction \[ {@A@}x+{@B@}+\frac{@C@}{x+1} \] [[input:ans]] [[validation:ans]]

]]> First write each term over a common denominator \[ {@(A*x+B)*D/D+C/D = ((A*x+B)*D+C)/D@}\] Then expand out brackets on the top and collect like terms to get \[ {@ev(expand((A*x+B)*D+C),simp)/D@}.\] 

]]> 1 0.1 0 A:ev(rand(4)+2,simp); B:ev(rand(4)+1,simp); C:ev(rand(4)+1,simp); D:x+1; p:A*x+B+C/D; ta:ev(factor(expand((A*x+B)*D+C)),simp)/D; [[feedback:prt1]]

]]> {@p = ta@}. 0 0 0 *10 none 1 i cos-1 lang [ 0 {"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}} ans algebraic ((A*x+B)*(x+1)+C)/x+1 20 1 0 0 1 1 1 1 1 prt1 1.0000000 0 1 0 SingleFrac ans ta 0 = 1.0000000 -1 1-0-T = 0.0000000 -1 1-0-F 1088093467 276430126 1612320671 1975502071 979415934 1094531026 1485717583 496467311 576765248 2121425648 1 ans ta prt1 1.0000000 0.0000000 1-0-T 2 ans p prt1 0.0000000 0.1000000 1-0-F 3 ans p+1 prt1 0.0000000 0.1000000 1-0-F 4 ans ev(expand((A*x+B)*D+C),simp)/D prt1 1.0000000 0.0000000 1-0-T