Solve for X,
writeExpressionFraction(NUMERATORS[0], DENOMINATORS[0]) =
writeExpressionFraction(NUMERATORS[1], DENOMINATORS[1]) +
writeExpressionFraction(NUMERATORS[2], DENOMINATORS[2])
X = \spaceCONSTANT / COEFFICIENT
First we need to find a common denominator for all the expressions. This means finding the least common multiple of
DENOMINATORS[0], DENOMINATORS[1] and DENOMINATORS[2].
The common denominator is COMMON_DENOM.
The denominator of the ordinalThrough20(i+1) term is already COMMON_DENOM, so we don't need to change it.
To get COMMON_DENOM in the denominator of the ordinalThrough20(i+1) term,
multiply it by \frac{MULTIPLES[i]}{MULTIPLES[i]}.
\qquad
writeExpressionFraction(NUMERATORS[i], DENOMINATORS[i]) \times
\dfrac{MULTIPLES[i]}{MULTIPLES[i]} =
writeExpressionFraction(PRODUCTS[i], COMMON_DENOM)
This gives us:
\qquad
writeExpressionFraction(PRODUCTS[0], COMMON_DENOM) =
writeExpressionFraction(PRODUCTS[1], COMMON_DENOM) +
writeExpressionFraction(PRODUCTS[2], COMMON_DENOM)
If we multiply both sides of the equation by COMMON_DENOM, we get:
\qquad PRODUCTS[0] = PRODUCTS[1] + PRODUCTS[2]\qquad PRODUCTS[0] = SUMS[0]\qquad
new KhanUtil.Term(COEFFICIENT, X) = CONSTANT
-CONSTANT = new KhanUtil.Term(-COEFFICIENT, X)
\qquad X = fraction(CONSTANT, COEFFICIENT, true, true)