# publicKhan/khan-exercises

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file 102 lines (93 sloc) 5.472 kb
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 `        Simplifying rational expressions 3

randVar()                    randVar()                    randRangeNonZero(-10, 10)
randRangeWeighted(-10, 10, 0, 0.5)                        randRangeWeighted(-10, 10, 0, 0.5)
new RationalExpression([[1, X], A])                    new RationalExpression([[1, X], B])                    new RationalExpression([[1, X], C])                    FACTOR1.multiply(FACTOR2)                    FACTOR1.multiply(FACTOR3)

Simplify the following expression and state the condition under which the simplification is valid:

Y = \dfrac{NUMERATOR}{DENOMINATOR}

FACTOR2.regex()                        FACTOR3.regex()                        -A

FACTOR2.multiply(-1).regex()                        FACTOR3.multiply(-1).regex()                        -A

Y =
a
a
\space X \neq a

a simplifed expression, like x + 2

First factor the expressions in the numerator and denominator.

\dfrac{NUMERATOR}{DENOMINATOR}                        = \dfrac{(FACTOR2)(FACTOR1)}{(FACTOR3)(FACTOR1)}

Notice that the term (FACTOR1) appears in both the numerator and denominator.

Dividing both the numerator and denominator by (FACTOR1) gives:

Y = \dfrac{FACTOR2}{FACTOR3} or more simply,                             Y = FACTOR2

Y = \dfrac{FACTOR2}{FACTOR3}

Since we divided by (FACTOR1), X \neq -A.

Y = writeExpressionFraction(FACTOR2, FACTOR3); \space X \neq -A

`
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The text passage contains a mathematical question about simplifying a rational expression and provides the answer to that question, including the condition under which the simplification is valid.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# publicKhan/khan-exercises

### Subversion checkout URL

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file 102 lines (93 sloc) 5.472 kb
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 `        Simplifying rational expressions 3

randVar()                    randVar()                    randRangeNonZero(-10, 10)
randRangeWeighted(-10, 10, 0, 0.5)                        randRangeWeighted(-10, 10, 0, 0.5)
new RationalExpression([[1, X], A])                    new RationalExpression([[1, X], B])                    new RationalExpression([[1, X], C])                    FACTOR1.multiply(FACTOR2)                    FACTOR1.multiply(FACTOR3)

Simplify the following expression and state the condition under which the simplification is valid:

Y = \dfrac{NUMERATOR}{DENOMINATOR}

FACTOR2.regex()                        FACTOR3.regex()                        -A

FACTOR2.multiply(-1).regex()                        FACTOR3.multiply(-1).regex()                        -A

Y =
a
a
\space X \neq a

a simplifed expression, like x + 2

First factor the expressions in the numerator and denominator.

\dfrac{NUMERATOR}{DENOMINATOR}                        = \dfrac{(FACTOR2)(FACTOR1)}{(FACTOR3)(FACTOR1)}

Notice that the term (FACTOR1) appears in both the numerator and denominator.

Dividing both the numerator and denominator by (FACTOR1) gives:

Y = \dfrac{FACTOR2}{FACTOR3} or more simply,                             Y = FACTOR2

Y = \dfrac{FACTOR2}{FACTOR3}

Since we divided by (FACTOR1), X \neq -A.

Y = writeExpressionFraction(FACTOR2, FACTOR3); \space X \neq -A

`
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user
The text passage contains a mathematical question about simplifying a rational expression and provides the answer to that question, including the condition under which the simplification is valid.

TYPE: SINGLE_QUESTION_WITH_ANSWER