# Include domain in rational expression question#43433

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merged 3 commits into from
+141 −42

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Redoing this pull request without the other unwanted commits.

I've added a new solution box to the question whenever you divide by an expression so you have to include the domain condition as part of your answer.

It's formatted using a table isn't isn't ideal especially as tabbing from one box to another goes in an unintuitive order, but it seemed better than creating a lot more divs and trying to line them up.

 petercollingridge `Include a solution box for the domain of the expression` `6ec8b01` petercollingridge `Remove redundant variable` `46e64e0` petercollingridge `Split final hint` `ead4c82`
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### Simplifying rational expressions 3 - wrong assumptions #43504

merged commit `4a17002` into Khan:master
Commits on Mar 17, 2013
1. petercollingridge committed
2. petercollingridge committed
3. petercollingridge committed
Showing with 141 additions and 42 deletions.
1. +141 −42 exercises/simplifying_rational_expressions_3.html
183 exercises/simplifying_rational_expressions_3.html
 @@ -18,6 +18,9 @@ padding-top: 1px; border-top: 1px solid black; } + #solutionarea .soln-dom { + padding-left: 3px; + } @@ -46,6 +49,52 @@ getExpressionRegex(-1, X, -B) getExpressionRegex(-1, X, -C) + +
+
+ POSITIVENUMERATOR + -A + POSITIVEDENOMINATOR +
+
+ NEGATIVENUMERATOR + -A + NEGATIVEDENOMINATOR +
+ +
+
+ +
+ Y = + + a + ; + \space X \neq a +
+ a +
+ + + + + + + + + + +
a simplifed expression, like x + 2
+ + +
+

The original expression has (X + A) in the denominator, + so is not defined when X = -A.

+
+

We must therefore include this condition with the simplified expression:

+ Y = \dfrac{FACTOR1}{FACTOR2}; \space X \neq -A +
+
@@ -59,6 +108,52 @@ getExpressionRegex(0, X, -B) getExpressionRegex(-1, X, -C)
+ +
+
+ POSITIVENUMERATOR + -A + POSITIVEDENOMINATOR +
+
+ NEGATIVENUMERATOR + -A + NEGATIVEDENOMINATOR +
+ +
+
+ +
+ Y = + + a + ; + \space X \neq a +
+ a +
+ + + + + + + + + + +
a simplifed expression, like x + 2
+ + +
+

The original expression has (X + A) in the denominator, + so is not defined when X = -A.

+
+

We must therefore include this condition with the simplified expression:

+ Y = \dfrac{FACTOR1}{FACTOR2}; \space X \neq -A +
+
@@ -72,45 +167,58 @@ getExpressionRegex(-1, X, -B) getExpressionRegex(0, X, -C)
- - -

Simplify the following expression:

-

Y = \dfrac{NUMERATOR}{DENOMINATOR}

-

You can assume X \neq 0.

+

Simplify the following expression:

+ +
+
+ POSITIVENUMERATOR + POSITIVEDENOMINATOR +
+
+ NEGATIVENUMERATOR + NEGATIVEDENOMINATOR +
-
-
- POSITIVENUMERATOR - POSITIVEDENOMINATOR -
-
- NEGATIVENUMERATOR - NEGATIVEDENOMINATOR -
-
-
- -
- Y = - - a -
- a -
- - - - - - - +
+
+ +
+ Y = + + a +
+ a +
+ + + + + + + + + +
a simplifed expression, like x + 2
+ + +
+
+

To remove the negative denominator, multiply the numerator and denominator by -1:

+
Y = \dfrac{-X + -B}{-C}
+
+
+

Dividing by -1 is the same thing as multiplying by -1, so the answer is:

+
Y = -X + -B
-

a simplifed expression, like x + 2

+ +

Simplify the following expression and state the domain:

+

Y = \dfrac{NUMERATOR}{DENOMINATOR}

+

First factor the expressions in the numerator and denominator.

@@ -123,7 +231,7 @@

Dividing both the numerator and denominator by (X + A) gives:

-
+
Y = \dfrac{FACTOR1}{FACTOR2} or more simply, Y = FACTOR1
@@ -131,15 +239,6 @@
-
-

To remove the negative denominator, multiply the numerator and denominator by -1:

-
Y = \dfrac{-X + -B}{-C}
-
-
-

Dividing by -1 is the same thing as multiplying by -1, so the answer is:

-
Y = -X + -B
-
-