Simplify the following expression:
\dfrac{NUMERATOR}{DENOMINATOR}
You can assume X \neq 0.
SOLUTION
\dfrac{NUMERATOR}{DENOMINATOR} =
\dfrac{COEFFICIENT1}{COEFFICIENT2} \cdot
\dfrac{X^DEGREE1}{X^DEGREE2}
To simplify \frac{COEFFICIENT1}{COEFFICIENT2}, find the greatest common factor (GCF) of
COEFFICIENT1 and COEFFICIENT2.
COEFFICIENT1 = getPrimeFactorization(COEFFICIENT1).join(" \\cdot ")
COEFFICIENT2 = getPrimeFactorization(COEFFICIENT2).join(" \\cdot ")
\mbox{GCD}(COEFFICIENT1, COEFFICIENT2)
= getPrimeFactorization(GCD).join(" \\cdot ") = GCD
\dfrac{COEFFICIENT1}{COEFFICIENT2} \cdot
\dfrac{X^DEGREE1}{X^DEGREE2} =
\dfrac{GCD \cdot COEFFICIENT1 / GCD}{GCD \cdot COEFFICIENT2 / GCD}
\cdot \dfrac{X^DEGREE1}{X^DEGREE2}
\phantom{
\dfrac{COEFFICIENT1}{COEFFICIENT2} \cdot \dfrac{DEGREE1}{DEGREE2}} =
fractionReduce(COEFFICIENT1 / GCD, COEFFICIENT2 / GCD)
\cdot \dfrac{X^DEGREE1}{X^DEGREE2}
\dfrac{X^DEGREE1}{X^DEGREE2} =
\dfrac{VARIABLE1.join(" \\cdot ")}{VARIABLE2.join(" \\cdot ")} =
POWERFRACTION
fractionReduce(COEFFICIENT1 / GCD, COEFFICIENT2 / GCD) \cdot POWERFRACTION = SOLUTIONFRACTION