randVar() randVar()
randRange( 2, 12 ) randRange( 1, 4 )
randRange( 1, 12 ) randRange( 1, 12 )
fraction(COEFFICIENT1, COEFFICIENT2, true, true) GCD * COEFFICIENT1 GCD * COEFFICIENT2 randFromArray( [0, 1] ) randFromArray( [0, 1] ) X + "^" + (DEGREE1 + MULTIPLEDEGREE) X + "^" + (DEGREE2 + MULTIPLEDEGREE) getSolution(1, 1, DEGREE1, DEGREE2, X) getVariableRegex(COEFFICIENT1, DEGREE1 - DEGREE2, X) getVariableRegex(COEFFICIENT2, DEGREE2 - DEGREE1, X) getSolution(COEFFICIENT1, COEFFICIENT2, DEGREE1, DEGREE2, X)

Simplify the following expression:

Y = \dfrac{NUMERATORCOEFFICIENTPOWER1} {DENOMINATORCOEFFICIENTPOWER2}

You can assume X \neq 0.

NUMERATORREGEX DENOMINATORREGEX
Y =
a simplified fraction, like 3x/4

\dfrac{NUMERATORCOEFFICIENTPOWER1} {DENOMINATORCOEFFICIENTPOWER2} = \dfrac{NUMERATORCOEFFICIENT}{DENOMINATORCOEFFICIENT} \cdot \dfrac{POWER1}{POWER2}

To simplify \frac{NUMERATORCOEFFICIENT}{DENOMINATORCOEFFICIENT}, find the greatest common factor (GCD) of NUMERATORCOEFFICIENT and DENOMINATORCOEFFICIENT.

NUMERATORCOEFFICIENT = getPrimeFactorization( NUMERATORCOEFFICIENT ).join( "\\cdot" )
DENOMINATORCOEFFICIENT = getPrimeFactorization( DENOMINATORCOEFFICIENT ).join( "\\cdot" )

\mbox{GCD}(NUMERATORCOEFFICIENT, DENOMINATORCOEFFICIENT) = getPrimeFactorization( GCD ).join( "\\cdot" ) = GCD

\dfrac{NUMERATORCOEFFICIENT}{DENOMINATORCOEFFICIENT} \cdot \dfrac{POWER1}{POWER2} = \dfrac{GCD \cdot COEFFICIENT1}{GCD \cdot COEFFICIENT2} \cdot \dfrac{POWER1}{POWER2}

\hphantom{\dfrac{NUMERATORCOEFFICIENT}{DENOMINATORCOEFFICIENT} \cdot \dfrac{POWER1}{POWER2}} = COEFFICIENTFRACTION \cdot \dfrac{POWER1}{POWER2}

\dfrac{POWER1}{POWER2} = POWERFRACTION

COEFFICIENTFRACTION \cdot \dfrac{POWER1}{POWER2} = COEFFICIENTFRACTION \cdot POWERFRACTION

\phantom{COEFFICIENTFRACTION \cdot \dfrac{POWER1}{POWER2}} = SOLUTION