document.write( "Question 888902: multiplication and division of rational expression;
\n" ); document.write( "[[q^3+4q^2-5q]/[q^2-2q+1]÷[q^2+q-2]/[q^4-8q]] * [q-4]/[q^2-2q+4] \n" ); document.write( "

Algebra.Com's Answer #537807 by algebrapro18(249) $\"\"$ $\"About$

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$\"%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29\"$ ÷ $\"%28q%5E2%2Bq-2%29%2F%28q%5E4-8q%29\"$ * $\"%28q-4%29%2F%28q%5E2-2q%2B4%29\"$
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\n" ); document.write( "\n" ); document.write( "First we need to remember that a rational expression divided by a rational expression is the same as a rational expression times the other expressions reciprocal. So:
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\n" ); document.write( "\n" ); document.write( " $\"%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29\"$ ÷ $\"%28q%5E2%2Bq-2%29%2F%28q%5E4-8q%29\"$ * $\"%28q-4%29%2F%28q%5E2-2q%2B4%29\"$
\n" ); document.write( "= $\"%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29\"$ * $\"%28q%5E4-8q%29%2F%28q%5E2%2Bq-2%29\"$ * $\"%28q-4%29%2F%28q%5E2-2q%2B4%29\"$
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\n" ); document.write( "\n" ); document.write( "Now we Factor all the parts of this expression to see if anything cancels out.\r
\n" ); document.write( "\n" ); document.write( " $\"%28q%5E3%2B4q%5E2-5q%29%2F%28q%5E2-2q%2B1%29\"$ * $\"%28q%5E4-8q%29%2F%28q%5E2%2Bq-2%29\"$ * $\"%28q-4%29%2F%28q%5E2-2q%2B4%29\"$
\n" ); document.write( "= $\"%28q%28q%5E2%2B4q-5%29%29%2F%28%28q-1%29%5E2%29\"$ * $\"%28q%28q%5E3-8%29%29%2F%28%28q-2%29%28q%2B1%29%29\"$ * $\"%28q-4%29%2F%28q%5E2-2q%2B4%29\"$
\n" ); document.write( "= $\"%28q%28%28q-1%29%28q%2B5%29%29%29%2F%28%28q-1%29%5E2%29\"$ * $\"%28q%28q-2%29%28q%5E2%2B2q%2B4%29%29%2F%28%28q-2%29%28q%2B1%29%29\"$ * $\"%28q-4%29%2F%28q%5E2-2q%2B4%29\"$
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\n" ); document.write( "\n" ); document.write( "Now we see that the $\"%28q-1%29\"$ terms in the first expression cancel out as well as the $\"%28q-2%29\"$ terms in the second expression. The $\"%28q%5E2%2B2q%2B4%29\"$ terms also cancel out so we are left with:
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\n" ); document.write( "\n" ); document.write( "= $\"%28q%28q%2B5%29%29%29%2F%28q-1%29\"$ * $\"q%2F%28q%2B1%29%29\"$ * $\"%28q-4%29%2F1\"$ \n" ); document.write( "

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