Can I write a function that carries out symbolic calculations in Python 2.7?

I'm currently transitioning from Java to Python and have taken on the task of trying to create a calculator that can carry out symbolic operations on infix-notated mathematical expressions (without using custom modules like Sympy). Currently, it's built to accept strings that are space delimited and can only carry out the (, ), +, -, *, and / operators. Unfortunately, I can't figure out the basic algorithm for simplifying symbolic expressions.

For example, given the string '2 * ( ( 9 / 6 ) + 6 * x )', my program should carry out the following steps:

1. 2 * ( 1.5 + 6 * x )
2. 3 + 12 * x

But I can't get the program to ignore the x when distributing the 2. In addition, how can I handle 'x * 6 / x' so it returns '6' after simplification?

EDIT: To clarify, by "symbolic" I meant that it will leave letters like "A" and "f" in the output while carrying out the remaining calculations.

EDIT 2: I (mostly) finished the code. I'm posting it here if anyone stumbles on this post in the future, or if any of you were curious.

    def reduceExpr(useArray):

        # Use Python's native eval() to compute if no letters are detected.
        if (not hasLetters(useArray)):
            return [calculate(useArray)] # Different from eval() because it returns string version of result

        # Base case. Returns useArray if the list size is 1 (i.e., it contains one string). 
        if (len(useArray) == 1):
            return useArray

        # Base case. Returns the space-joined elements of useArray as a list with one string.
        if (len(useArray) == 3):
            return [' '.join(useArray)]

        # Checks to see if parentheses are present in the expression & sets.
        # Counts number of parentheses & keeps track of first ( found. 
        parentheses = 0
        leftIdx = -1

        # This try/except block is essentially an if/else block. Since useArray.index('(') triggers a KeyError
        # if it can't find '(' in useArray, the next line is not carried out, and parentheses is not incremented.
        try:
            leftIdx = useArray.index('(')
            parentheses += 1
        except Exception:
            pass

        # If a KeyError was returned, leftIdx = -1 and rightIdx = parentheses = 0.
        rightIdx = leftIdx + 1

        while (parentheses > 0):
            if (useArray[rightIdx] == '('):
                parentheses += 1
            elif (useArray[rightIdx] == ')'):
                parentheses -= 1
            rightIdx += 1

        # Provided parentheses pair isn't empty, runs contents through again; else, removes the parentheses
        if (leftIdx > -1 and rightIdx - leftIdx > 2):
            return reduceExpr(useArray[:leftIdx] + [' '.join(['(',reduceExpr(useArray[leftIdx+1:rightIdx-1])[0],')'])] + useArray[rightIdx:])
        elif (leftIdx > -1):
            return reduceExpr(useArray[:leftIdx] + useArray[rightIdx:])

        # If operator is + or -, hold the first two elements and process the rest of the list first
        if isAddSub(useArray[1]):
            return reduceExpr(useArray[:2] + reduceExpr(useArray[2:]))
        # Else, if operator is * or /, process the first 3 elements first, then the rest of the list
        elif isMultDiv(useArray[1]):
            return reduceExpr(reduceExpr(useArray[:3]) + useArray[3:])
        # Just placed this so the compiler wouldn't complain that the function had no return (since this was called by yet another function).
        return None