document.write( "Question 287735: Construct and Simplify the difference quotient \"+%28f%28x%2Bh%29-f%28x%29%29%2Fh+\"
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Algebra.Com's Answer #208505 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Construct and Simplify the difference quotient \"+%28f%28x%2Bh%29-f%28x%29%29%2Fh+\"
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document.write( "Let's do it piece by piece. \r\n" );
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document.write( "\"+%28highlight%28f%28x%2Bh%29%29-f%28x%29%29%2Fh+\"\r\n" );
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document.write( "Let's first find \"highlight%28%22f%28x%2Bh%29%22%29%29\" using\r\n" );
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document.write( "\"+f%28red%28x%29%29=2red%28x%29%5E2-red%28x%29+\"\r\n" );
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document.write( "In place of those red \"red%28x%29\"'s, let's put \"red%28%28x%2Bh%29%29\"\r\n" );
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document.write( "\"+f%28red%28x%2Bh%29%29=2red%28%28x%2Bh%29%29%5E2-red%28%28x%2Bh%29%29+\"\r\n" );
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document.write( "Simplify the right side:\r\n" );
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document.write( "\"+f%28x%2Bh%29=2%28x%2Bh%29%5E2-%28x%2Bh%29+\"\r\n" );
document.write( "\"+f%28x%2Bh%29=2%28x%2Bh%29%28x%2Bh%29-%28x%2Bh%29+\"\r\n" );
document.write( "\"+f%28x%2Bh%29=2%28x%5E2%2B2hx%2Bh%5E2%29-x-h+\"\r\n" );
document.write( "\"+f%28x%2Bh%29=2x%5E2%2B4hx%2B2h%5E2-x-h+\"\r\n" );
document.write( "\"+f%28x%2Bh%29=2x%5E2%2B4hx%2B2h%5E2-x-h+\"\r\n" );
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document.write( "Replace the \"f%28x%2Bh%29\" in\r\n" );
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document.write( "\"+%28highlight%28f%28x%2Bh%29%29-f%28x%29%29%2Fh+\"\r\n" );
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document.write( "by \"highlight%282x%5E2%2B4hx%2B2h%5E2-x-h%29+\"\r\n" );
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document.write( "\"+%28highlight%282x%5E2%2B4hx%2B2h%5E2-x-h%29-f%28x%29%29%2Fh+\"\r\n" );
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document.write( "Next we need to replace replace the \"highlight%28f%28x%29%29\" in \r\n" );
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document.write( "\"+%282x%5E2%2B4hx%2B2h%5E2-x-h-highlight%28f%28x%29%29+%29%2Fh+\"\r\n" );
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document.write( "by what we are given for \"%22f%28x%29%22\", namely \"f%28x%29=highlight%28%282x%5E2-x%29+%29+\"\r\n" );
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document.write( "\"+%282x%5E2%2B4hx%2B2h%5E2-x-h-highlight%28%282x%5E2-x%29%29+%29%2Fh+\"\r\n" );
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document.write( "Now we simplify:\r\n" );
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document.write( "\"+%282x%5E2%2B4hx%2B2h%5E2-x-h-%282x%5E2-x%29+%29%2Fh+\"\r\n" );
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document.write( "\"+%282x%5E2%2B4hx%2B2h%5E2-x-h-2x%5E2%2Bx+%29%2Fh+\"\r\n" );
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document.write( "Cancel the \"2x%5E2\" and the \"-2x%5E2\"\r\n" );
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document.write( "\"+%28cross%282x%5E2%29%2B4hx%2B2h%5E2-x-h-cross%282x%5E2%29%2Bx+%29%2Fh+\"\r\n" );
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document.write( "\"+%284hx%2B2h%5E2-x-h%2Bx+%29%2Fh+\"\r\n" );
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document.write( "Cancel the \"-x\" and the \"%22%22%2Bx\"\r\n" );
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document.write( "\"+%284hx%2B2h%5E2-cross%28x%29-h%2Bcross%28x%29+%29%2Fh+\"\r\n" );
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document.write( "\"+%284hx%2B2h%5E2-h+%29%2Fh+\"\r\n" );
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document.write( "Factor \"h\" out of the numerator:\r\n" );
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document.write( "\"+%28h%284x%2B2h-1%29+%29%2Fh+\"\r\n" );
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document.write( "Cancel the \"h\"'s\r\n" );
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document.write( "\"+%28cross%28h%29%284x%2B2h-1%29+%29%2Fcross%28h%29+\"\r\n" );
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document.write( "\"4x%2B2h-1\"\r\n" );
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document.write( "That's it!\r\n" );
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document.write( "Edwin
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