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Fractions don't have a common denominator. Need to find one. Addition and subtraction 50:50 split.

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Express the following as a single fraction (using / as the fraction bar).

", "advice": "

We need to get the denominators to be the same, preferably the lowest common denominator, at which point, we can simply addsubtract the new numerators and put the result over the common denominator.

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Since $\\var{den1}=\\var{cf}\\times\\var{extrafactor[0]}$ and $\\var{den2}=\\var{cf}\\times \\var{extrafactor[1]}$ the lowest common denominator will be the product $\\var{cf}\\times \\var{extrafactor[0]}\\times \\var{extrafactor[1]}$, that is, $\\var{ansden}$. Therefore, we will multiply the first fraction by $\\frac{\\var{extrafactor[1]}}{\\var{extrafactor[1]}}$ and the second fraction by $\\frac{\\var{extrafactor[0]}}{\\var{extrafactor[0]}}$ as follows.

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}+\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}\\times \\var{extrafactor[1]}}{\\var{den1}\\times \\var{extrafactor[1]}}+\\dfrac{\\var{num2}\\times \\var{extrafactor[0]}}{\\var{den2}\\times \\var{extrafactor[0]}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}}{\\var{ansden}}+\\dfrac{\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}+\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}-\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}\\times \\var{extrafactor[1]}}{\\var{den1}\\times \\var{extrafactor[1]}}-\\dfrac{\\var{num2}\\times \\var{extrafactor[0]}}{\\var{den2}\\times \\var{extrafactor[0]}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}}{\\var{ansden}}-\\dfrac{\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}-\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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Since $\\var{den2}=\\var{cf}\\times \\var{extrafactor[1]}$ and the other denominator is $\\var{den1}$, the lowest common denominator will be the product $\\var{cf}\\times \\var{extrafactor[1]}$, that is, $\\var{ansden}$. Therefore, we will multiply the first fraction by $\\frac{\\var{extrafactor[1]}}{\\var{extrafactor[1]}}$ as follows.

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}+\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}\\times \\var{extrafactor[1]}}{\\var{den1}\\times \\var{extrafactor[1]}}+\\dfrac{\\var{num2}}{\\var{den2}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}}{\\var{ansden}}+\\dfrac{\\var{num2}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}+\\var{num2}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}-\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}\\times \\var{extrafactor[1]}}{\\var{den1}\\times \\var{extrafactor[1]}}-\\dfrac{\\var{num2}}{\\var{den2}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}}{\\var{ansden}}-\\dfrac{\\var{num2}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}-\\var{num2}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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Since $\\var{den1}=\\var{cf}\\times\\var{extrafactor[0]}$ and the other denominator is $\\var{den2}$, the lowest common denominator will be the product $\\var{cf}\\times \\var{extrafactor[0]}$, that is, $\\var{ansden}$. Therefore, we will multiply the second fraction by $\\frac{\\var{extrafactor[0]}}{\\var{extrafactor[0]}}$ as follows.

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}+\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}}{\\var{den1}}+\\dfrac{\\var{num2}\\times \\var{extrafactor[0]}}{\\var{den2}\\times \\var{extrafactor[0]}}\\\\[3pt]&=\\dfrac{\\var{num1}}{\\var{ansden}}+\\dfrac{\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1}+\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}-\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}}{\\var{den1}}-\\dfrac{\\var{num2}\\times \\var{extrafactor[0]}}{\\var{den2}\\times \\var{extrafactor[0]}}\\\\[3pt]&=\\dfrac{\\var{num1}}{\\var{ansden}}-\\dfrac{\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1}-\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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Since there are no common factors between the two denominators (other than $1$) the lowest common denominator will just be the product of the two denominators. Therefore, we will multiply the first fraction by $\\frac{\\var{extrafactor[1]}}{\\var{extrafactor[1]}}$ and the second fraction by $\\frac{\\var{extrafactor[0]}}{\\var{extrafactor[0]}}$ as follows.

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}+\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}\\times \\var{extrafactor[1]}}{\\var{den1}\\times \\var{extrafactor[1]}}+\\dfrac{\\var{num2}\\times \\var{extrafactor[0]}}{\\var{den2}\\times \\var{extrafactor[0]}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}}{\\var{ansden}}+\\dfrac{\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}+\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den1}}-\\dfrac{\\var{num2}}{\\var{den2}}&=\\dfrac{\\var{num1}\\times \\var{extrafactor[1]}}{\\var{den1}\\times \\var{extrafactor[1]}}-\\dfrac{\\var{num2}\\times \\var{extrafactor[0]}}{\\var{den2}\\times \\var{extrafactor[0]}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}}{\\var{ansden}}-\\dfrac{\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{num1*extrafactor[1]}-\\var{num2*extrafactor[0]}}{\\var{ansden}}\\\\[3pt]&=\\dfrac{\\var{ansNum}}{\\var{ansden}}\\end{align*}$

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adding or subtracting

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common factor of denominators

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extra factors in the denominators

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$\\dfrac{\\var{num1}}{\\var{den1}}+\\dfrac{\\var{num2}}{\\var{den2}}$ $\\dfrac{\\var{num1}}{\\var{den1}}-\\dfrac{\\var{num2}}{\\var{den2}}$  $=$ [[0]]

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