AlgMap-8.10 Express the following as a single fraction in it's lowest terms: \[\frac{@ev(a*(u+v),simp)@}{@c@}+\frac{@ev(b*(u+v),simp)@}{@d@}. \]
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]]> You can treat compound terms, \({@ev(u+v,simp)@}\) as a single variable when simplifying the above expression. Alternatively you can substitute \(u = {@ev(u+v,simp)@}\) and thereby simplify with a single variable:
\[\frac{@ev(a*(u+v),simp)@}{@c@}+\frac{@ev(b*(u+v),simp)@}{@d@} = \frac{{@a@}u}{@c@}+\frac{{@b@}u}{@d@} = \frac{{@ev(a*(lcm(c,d)/c),simp)@}u}{@ev(lcm(c,d),simp)@}+\frac{{@ev(b*(lcm(c,d)/d),simp)@}u}{@ev(lcm(c,d),simp)@} = \frac{{@ev((a*(lcm(c,d)/c)+b*(lcm(c,d)/d)),simp)@}u}{@ev(lcm(c,d),simp)@} = {@fta@}. \]

]]> 1 0.1 0 u:ev(rand([x,t]),simp); v:ev(rand([y,z]),simp); a:ev(rand(4)+6,simp); b:ev(rand(4)+7,simp); c:ev(rand(3)+2,simp); d:ev(c+1,simp); ta:ev((ratsimp(a*(u+v)/c+b*(u+v)/d)),simp); fta:ev(factor(ta),simp); [[feedback:prt1]]

]]> \[\frac{@ev(a*(u+v),simp)@}{@c@}+\frac{@ev(b*(u+v),simp)@}{@d@} = {@ta@}. \] 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 ta 15 1 0 0 expand 1 1 1 1 1 prt1 1.0000000 0 1 0 SingleFrac ans fta u 0 = 1.0000000 -1 1-0-T = 0.0000000 1 1-0-F 1 AlgEquiv ans (a*(u+v)+b*(u+v))/(c+d) 0 = 0.0000000 -1 1-1-T You cannot simply add the numerators and denominators when adding fractions. You need to find a common denominator and then add the fractions. One option is to use the general rule: \(\frac{a}{c}+\frac{b}{d} = \frac{ad+cd}{cd} \)

]]> = 0.0000000 -1 1-1-F 496178535 1856951054 1715030049 477684187 270137545 690555843 1 ans fta prt1 1.0000000 0.0000000 1-0-T 2 ans ta prt1 1.0000000 0.0000000 1-0-T 3 ans (a*(u+v)/c+b*(u+v)/d) prt1 0.0000000 0.1000000 1-1-F 4 ans ev((a*(u+v)+b*(u+v))/(c+d),simp) prt1 0.0000000 0.1000000 1-1-T