document.write( "Question 73765: solve & check the equation, beginning algebra 6th edition chpt 5.5. i have no clue as to where to start on this problem. i am completely stuck on this problem, any help with this problem will be appreciated.
\n" ); document.write( "5 / x + 2 + 2 / x ^ 2 + 7 x + 6 = 3 / x + 1\r
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Algebra.Com's Answer #52998 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"5+%2F+x+%2B+2++%2B++2+%2F+x+%5E+2++%2B++7+x+%2B+6++=++3+%2F+x+%2B+1\"
\n" ); document.write( "\"x%5E2%285+%2F+x+%2B+2++%2B++2+%2F+x+%5E+2++%2B++7+x+%2B+6%29++=++x%5E2%283+%2F+x+%2B+1%29\"To get rid of the fractions, multiply everything by the LCD (the LCD is x^2)
\n" ); document.write( "\"5x+%2B+2x%5E2++%2B++2++%2B++7x%5E3+%2B+6x%5E2++=++3x+%2B+x%5E2\"Distribute the x^2
\n" ); document.write( "\"7x%5E3+%2B+8x%5E2+%2B+5x+++%2B++2+=++3x+%2B+x%5E2\"Combine like terms
\n" ); document.write( "\"7x%5E3+%2B+8x%5E2+-x%5E2+%2B+5x+-3x++%2B++2+=+0\"Get everything to one side
\n" ); document.write( "\"highlight%287x%5E3+%2B+7x%5E2%29+%2B+highlight%282x++%2B++2%29+=+0\"Group the highlighted terms
\n" ); document.write( "\"7x%5E2%28x+%2B+1%29+%2B+2%28x++%2B++1%29+=+0\"Factor out a 7x^2 out of the 1st group of parenthesis and factor out a 2 out of the 2nd group of parenthesis. Notice how we have a common term of (x+1). We can combine them now
\n" ); document.write( "\"%287x%5E2%2B2%29%28x+%2B+1%29=+0\"Combine the terms. If we let y=(x+1) it would look like \"7x%5E2y%2B2y=%287x%5E2%2B2%29%28y%29\" Now we can solve for x.
\n" ); document.write( "\"%287x%5E2%2B2%29%28x+%2B+1%29=+0\" Isolate each factor and solve:
\n" ); document.write( "\"%28x+%2B+1%29=+0\"
\n" ); document.write( "\"x=-1\"There's our answer
\n" ); document.write( "\"%287x%5E2%2B2%29=0\"
\n" ); document.write( "\"7x%5E2=-2\"
\n" ); document.write( "\"x%5E2=-2%2F7\"
\n" ); document.write( "\"x=sqrt%28-2%2F7%29\"This answer will not be real (I don't know if you know about complex roots yet), so I would ignore this factor.
\n" ); document.write( "So our answer is x=-1
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\n" ); document.write( "Check
\n" ); document.write( "\"5+%2F+x+%2B+2++%2B++2+%2F+x+%5E+2++%2B++7+x+%2B+6++=++3+%2F+x+%2B+1\"Plug in x=-1
\n" ); document.write( "\"5+%2F%28-1%29+%2B+2++%2B++2+%2F%28-1%29%5E+2++%2B++7%28-1%29+%2B+6++=++3+%2F%28-1%29%2B+1\"
\n" ); document.write( "\"-5+%2B+2++%2B++2++-7+%2B+6++=++-3%2B+1\"
\n" ); document.write( "\"-3++%2B++-5+%2B+6++=++-2\"
\n" ); document.write( "\"-2++=++-2\"Works \n" ); document.write( "

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