Learning Guide Learning Guide

5.1 Mathematical Manipulations • 155combine: combining with respect to cmbpluscombine: combining with respect to cmbpwrcombine: combining with respect to power∫x 2 + 1 dxThe expand command applies most of these transformation rules in theother direction. See this section, page 146.Factored Normal FormIf an expression contains fractions, you may find it useful to turn theexpression into one large fraction, and cancel common factors in the numeratorand denominator. The normal command performs this process,which often leads to simpler expressions.> normal( x + 1/x );x 2 + 1x> expr := x/(x+1) + 1/x + 1/(1+x);expr :=xx + 1 + 1 x + 1x + 1> normal( expr );x + 1x> expr := (x^2 - y^2) / (x-y)^3;expr := x2 − y 2(x − y) 3> normal( expr );x + y(x − y) 2