document.write( "Question 94240: Can you please help me. The problem says perform the indicated operation and simplify the result. Leave answers in factored form: A. $\"%28%2812%29%2F%28x%5E2-x%29%29+%2A%28%28x%5E2-1%29%2F%284x-2%29%29\"$ b. $\"%28x%29%2F%28x-3%29-%28x%2B1%29%2F%28x%5E2%2B5x-24%29\"$ c. $\"%281%2Fh%29%2A%281%2F%28x%2Bh%29-1%2Fx%29\"$ d. $\"%285%284x%2B1%29-4%285x-2%29%29%2F%285x-2%29%5E2\"$ If possible could you show me the steps and rules used to complete these. Thank you sooooo much!!! \n" ); document.write( "

Algebra.Com's Answer #68650 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Can you please help me. The problem says perform the indicated operation and simplify the result. Leave answers in factored form:
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\n" ); document.write( "A. $\"12%2F%28%28x%5E2-x%29%29\"$ * $\"%28%28x%5E2-1%29%29%2F%28%284x-2%29%29\"$
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\n" ); document.write( "Step 1 is to see what can be factored, often you will have the same factors
\n" ); document.write( "and can see some that can be factored out, which simplifies things.
\n" ); document.write( "Note that (x^2-1) is the difference of squares
\n" ); document.write( "In this one we can do this:
\n" ); document.write( " $\"12%2F%28x%28x-1%29%29\"$ * $\"%28%28x-1%29%28x%2B1%29%29%2F%282%282x-1%29%29\"$
\n" ); document.write( ":
\n" ); document.write( "Cancel the (x-1)'s. The 2 will cancel into the 12. Leaving us with:
\n" ); document.write( " $\"6%2Fx\"$ * $\"%28%28x%2B1%29%29%2F%28%282x-1%29%29\"$ = $\"%286%28x%2B1%29%29%2F%28x%282x-1%29%29\"$
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\n" ); document.write( " b. $\"x%2F%28%28x-3%29%29\"$ - $\"%28%28x%2B1%29%29%2F%28%28x%5E2%2B5x-24%29%29\"$
\n" ); document.write( ":
\n" ); document.write( " $\"x%2F%28%28x-3%29%29\"$ - $\"%28%28x%2B1%29%29%2F%28%28x%2B8%29%28x-3%29%29\"$
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\n" ); document.write( "Common denominator would be (x-3)(x+8), so we can have:
\n" ); document.write( " $\"%28x%28x%2B8%29+-+%28x%2B1%29%29%2F%28%28x-3%29%28x%2B8%29%29\"$ = $\"%28x%5E2+%2B+8x+-+x+-+1%29%2F%28%28x-3%29%28x%2B8%29%29\"$ = $\"%28x%5E2+%2B+7x+-+1%29%2F%28%28x-3%29%28x%2B8%29%29\"$
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\n" ); document.write( "the final numerator won't factor so that's about all we can do with it
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\n" ); document.write( " c. Here we want to place the second expression over a common denominator 1st.
\n" ); document.write( " $\"1%2Fh\"$ * $\"%281%2F%28%28x%2Bh%29%29+-+1%2Fx%29\"$ = $\"1%2Fh\"$ * $\"%281x+-+1%28x%2Bh%29%29%2F%28x%28x%2Bh%29%29\"$ = $\"1%2Fh\"$ * $\"%281x+-+1x+-+h%29%2F%28x%28x%2Bh%29%29\"$ = $\"1%2Fh\"$ * $\"%28-h%29%2F%28x%28x%2Bh%29%29\"$
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\n" ); document.write( "Cancel h into -h and you have:
\n" ); document.write( " $\"%28-1%29%2F%28x%28x%2Bh%29%29\"$ = $\"-1%2F%28x%28x%2Bh%29%29\"$
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\n" ); document.write( " d. Multiply what's inside the brackets, remember a minus outside the brackets
\n" ); document.write( "changes the signs inside the brackets.
\n" ); document.write( " $\"%285%284x%2B1%29-4%285x-2%29%29%2F%28%285x-2%29%5E2%29\"$ = $\"%2820x+%2B+5+-+20+x+%2B+8%29%2F%28%285x-2%29%285x-2%29%29\"$ = $\"%2813%29%2F%28%285x-2%29%285x-2%29%29\"$
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\n" ); document.write( "If possible could you show me the steps and rules used to complete these
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\n" ); document.write( "The rules are much the same as for dealing with numerical fractions,
\n" ); document.write( "Remember the rule about a negative outside the brackets.
\n" ); document.write( "When factoring, look for the difference of squares for example:
\n" ); document.write( "(x^2 - 4) factors to (x+2)(x-2); and 4x^2 - 9) factors to (2x+3)(2x-3)
\n" ); document.write( "Use a step-by-step approach
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\n" ); document.write( "Any questions about what we did here? \n" ); document.write( "

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