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Add hints to explain the domain
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petercollingridge committed Mar 16, 2013
1 parent e5d8212 commit 8fffb16
Showing 1 changed file with 34 additions and 12 deletions.
46 changes: 34 additions & 12 deletions exercises/simplifying_rational_expressions_3.html
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padding-top: 1px;
border-top: 1px solid black;
}
#solutionarea .soln-dom {
padding-left: 3px;
}
</style>
</head>
<body>
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<div class="example">a simplifed expression, like <code>x + 2</code></div>
</div>

<div class="hints" data-apply="appendContents">
<div>
<p>The original expression has <code>(<var>X</var> + <var>A</var>)</code> in the denominator,
so is not defined when <code><var>X</var> = <var>-A</var></code>.</p>
We must therefore include this condition with the simplified expression:</p>
<code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}; \space
<var>X</var> \neq <var>-A</var></code>
</div>
</div>
</div>

<div id="top-constant">
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<code><var>Y</var> = </code>
</td>
<td class="soln-top">
<span class="sol short32">a</span>
<span class="sol short40">a</span>
</td>
<td rowspan="2">;
<code> \space <var>X</var> \neq </code><span class="sol soln-dom short32">a</span>
</td>
</tr>
<tr>
<td class="soln-bot">
<span class="sol short32" data-fallback="1">a</span>
<span class="sol short40" data-fallback="1">a</span>
</td>
</tr>
</table>
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<div class="example">a simplifed expression, like <code>x + 2</code></div>
</div>

<div class="hints" data-apply="appendContents">
<div>
<p>The original expression has <code>(<var>X</var> + <var>A</var>)</code> in the denominator,
so is not defined when <code><var>X</var> = <var>-A</var></code>.</p>
We must therefore include this condition with the simplified expression:</p>
<code><var>Y</var> = \dfrac{<var>FACTOR1</var>}{<var>FACTOR2</var>}; \space
<var>X</var> \neq <var>-A</var></code>
</div>
</div>
</div>

<div id="bottom-constant">
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<div class="example">a simplifed expression, like <code>x + 2</code></div>
</div>

<div class="hints" data-apply="appendContents">
<div data-if="FACTOR2 < -1">
<p>To remove the negative denominator, multiply the numerator and denominator by -1:</p>
<div><code><var>Y</var> = \dfrac{-<var>X</var> + <var>-B</var>}{<var>-C</var>}</code></div>
</div>
<div data-if="FACTOR2 === -1">
<p>Dividing by -1 is the same thing as multiplying by -1, so the answer is:</p>
<div><code><var>Y</var> = -<var>X</var> + <var>-B</var></code></div>
</div>
</div>

</div>

</div>

<p class="problem">Simplify the following expression and state the domain:</p>
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</div>
</div>

<div data-if="FACTOR2 < -1">
<p>To remove the negative denominator, multiply the numerator and denominator by -1:</p>
<div><code><var>Y</var> = \dfrac{-<var>X</var> + <var>-B</var>}{<var>-C</var>}</code></div>
</div>
<div data-if="FACTOR2 === -1">
<p>Dividing by -1 is the same thing as multiplying by -1, so the answer is:</p>
<div><code><var>Y</var> = -<var>X</var> + <var>-B</var></code></div>
</div>

</div>
</div>
</body>
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