randVar() randVar() randRangeWeighted(1, 5, 1, 0.25) randRangeNonZero(-10, 10) new RationalExpression([[COEFFICIENT, X], CONSTANT]) function(){if(rand(2))var e=new Term(randRangeWeighted(1,8,1,.25),X),r=new Term(randRange(1,10));else var e=new Term(randRangeExclude(-10,10,[-1,0,1])),r=rand(2)?new Term(randRange(1,10)):new Term(randRangeWeighted(1,8,1,.25),X);if(e.string=e.toString(),e.parenthesise=!1,rand(2))var a=new Term(randRangeWeighted(1,8,1,.25),X),n=new Term(randRange(1,10));else var a=new Term(randRangeExclude(-10,10,[-1,0,1])),n=rand(2)?new Term(randRange(1,10)):new Term(randRangeWeighted(1,8,1,.25),X);a.string=a.toString(),a.parenthesise=!1;var t=COMMON_TERM.multiply(n),i=COMMON_TERM.multiply(r);return rand(2)?(t.string=t.toString(),t.parenthesise=!0):(t.string=t.toStringFactored(),t.parenthesise="1"===n.toString()),rand(2)?(i.string=i.toString(),i.parenthesise=!0):(i.string=i.toStringFactored(),i.parenthesise="1"===r.toString()),rand(2)?[{numerator:t,denominator:e},{numerator:a,denominator:i},{numerator:[a,n],denominator:[e,r]}]:[{numerator:e,denominator:t},{numerator:i,denominator:a},{numerator:[e,r],denominator:[a,n]}]}() FRACTION1.numerator.multiply(FRACTION2.numerator) FRACTION1.denominator.multiply(FRACTION2.denominator) FRACTION3.numerator[0].multiply(FRACTION3.numerator[1]) FRACTION3.denominator[0].multiply(FRACTION3.denominator[1]) DENOMTERM.coefficient>0?NUMERTERM.getGCD(DENOMTERM):NUMERTERM.getGCD(DENOMTERM).multiply(-1) NUMERTERM.divide(FACTOR) DENOMTERM.divide(FACTOR)

Simplifica la siguiente expresión e indica bajo qué condición la simplificación es válida. Puedes suponer que X \neq 0.

Y = \dfrac{FRACTION1.numerator.string}{FRACTION1.denominator.string} \times \dfrac{FRACTION2.numerator.string}{FRACTION2.denominator.string}

Y = \dfrac{FRACTION1.numerator.string}{FRACTION1.denominator.string} \div \dfrac{FRACTION2.denominator.string}{FRACTION2.numerator.string}

Dividir entre una expresión es lo mismo que multiplicar entre su inverso.

Y = \dfrac{FRACTION1.numerator.string}{FRACTION1.denominator.string} \times \dfrac{FRACTION2.numerator.string}{FRACTION2.denominator.string}

NUMERSOL.regex() DENOMSOL.regex() -CONSTANT/COEFFICIENT
NUMERSOL.multiply(-1).regex() DENOMSOL.multiply(-1).regex() -CONSTANT/COEFFICIENT
Y =
a
a
\space X \neq \space a

Al multiplicar fracciones, multiplicamos los numeradores y denominadores.

Y = \dfrac{ (FRACTION1.numerator.string) FRACTION1.numerator.string \times (FRACTION2.numerator.string) FRACTION2.numerator.string } { (FRACTION1.denominator.string) FRACTION1.denominator.string \times (FRACTION2.denominator.string) FRACTION2.denominator.string }

Y = \dfrac {FRACTION3.numerator[0] \times FRACTION3.numerator[1](COMMON_TERM)} {FRACTION3.denominator[0] \times FRACTION3.denominator[1](COMMON_TERM)}

Y = \dfrac{NUMERTERM(COMMON_TERM)}{DENOMTERM(COMMON_TERM)}

Podemos cancelar el COMMON_TERM siempre y cuando COMMON_TERM \neq 0.

Por lo tanto X \neq fraction(-CONSTANT, COEFFICIENT, true, true).

Y = \dfrac{NUMERTERM \cancel{(COMMON_TERM})}{DENOMTERM \cancel{(COMMON_TERM)}} = writeExpressionFraction(NUMERTERM, DENOMTERM) = writeExpressionFraction(NUMERSOL, DENOMSOL) NUMERSOL