document.write( "Question 1032246: 1. Create two different rational polynomial expressions with the following constraints:
\n" ); document.write( "•one expression is undefined when x = 4,
\n" ); document.write( "•the other is undefined when x = ‒2 or 0.\r
\n" ); document.write( "\n" ); document.write( "Then, rewrite both as equivalent expressions, with a common denominator.\r
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\n" ); document.write( "\n" ); document.write( "2. The expression G over H is multiplied with another rational expression, and the product is 2. What is the other rational expression?\r
\n" ); document.write( "\n" ); document.write( "(Note: Please show all work so that I can understand your logic. Thank you.) \n" ); document.write( "
Algebra.Com's Answer #647050 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
1.
\n" ); document.write( "\"1%2F%28x-4%29\" is a rational polynomial expression,
\n" ); document.write( "with the polynomial \"1\" as the numerator,
\n" ); document.write( "and the polynomial \"x-4\" as the denominator.
\n" ); document.write( "It is undefined when \"x+=+4\" .
\n" ); document.write( "For those having qualms about calling \"1\" a polynomial,
\n" ); document.write( "we could use a fancier denominator, and write something like
\n" ); document.write( "\"%28x-2%29%2F%28x-4%29\" (probably a safer choice),
\n" ); document.write( "or even \"%28x-4%29%2F%28x-4%29\" (which is not equivalent to \"1\" , unless you specify \"except for \"x=4\" \", so you cannot simplify).
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\n" ); document.write( "\"1%2F%28x%5E2%2B2x%29=1%2F%28x%28x%2B2%29%29\" is a rational polynomial expression,
\n" ); document.write( "with the polynomial \"1\" as the numerator,
\n" ); document.write( "and the polynomial \"x%5E2%2B2x\" as the denominator.
\n" ); document.write( "It is undefined when \"x=-2\" , and when \"x=0\" .
\n" ); document.write( "For those having qualms about calling \"1\" a polynomial,
\n" ); document.write( "we could use a fancier denominator, and write something like
\n" ); document.write( "\"%28x%2B4%29%2F%28x%5E2%2B2x%29\" .
\n" ); document.write( "
\n" ); document.write( "For a common denominator,
\n" ); document.write( "we need to include in that common denominator all the factors of the two denominators.
\n" ); document.write( "So, the common denominator would be
\n" ); document.write( "\"x%28x%2B2%29%28x-4%29=x%28x%5E2-2x-8%29=x%5E3-2x%5E2-8x\" .
\n" ); document.write( "To get equivalent rational expression, we need to multiply numerator and denominator times the same factor(s).
\n" ); document.write( "So,
\n" ); document.write( "\"1%2F%28x-4%29\" is equivalent to \"x%28x%2B2%29%2F%28x%28x%2B2%29%28x-4%29%29=%28x%5E2%2B2x%29%2F%28x%5E3-2x%5E2-8x%29\" .
\n" ); document.write( "\"%28x-2%29%2F%28x-4%29\" is equivalent to .
\n" ); document.write( "\"%28x-4%29%2F%28x-4%29\" is equivalent to .
\n" ); document.write( "\"1%2F%28x%5E2%2B2x%29=1%2F%28x%28x%2B2%29%29\" is equivalent to \"%28x-4%29%2F%28x%28x%2B2%29%28x-4%29%29=%28x-4%29%2F%28x%5E3-2x%5E2-8x%29\" .
\n" ); document.write( "\"%28x%2B4%29%2F%28x%5E2%2B2x%29=%28x%2B4%29%2F%28x%28x%2B2%29%29\" is equivalent to \"%28x%2B4%29%28x-4%29%2F%28x%28x%2B2%29%28x-4%29%29=%28x%5E2-16%29%2F%28x%5E3-2x%5E2-8x%29\" .
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\n" ); document.write( "2. IF \"G%28x%29%2FH%28x%29\" is an expression defined for all values of \"x\" ,
\n" ); document.write( "which means that \"H%28x%29=0\" has no real solution, AND
\n" ); document.write( "IF \"G%28x%29=0\" has no real solution either,
\n" ); document.write( "\"H%28x%29\" and \"G%28x%29\" are \"safe\" to use as denominators.
\n" ); document.write( "Then, multiplying \"G%28x%29%2FH%28x%29\" times \"2H%28x%29%2FG%28x%29\" will yield
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