document.write( "Question 988368: I am trying to solve this problem but my answer is not the answer in the book. Can you help me figure it out? Here is the equation:\r
\n" ); document.write( "\n" ); document.write( "x/(x-3) + 4/(x+5)=8x/((x-3)(x+5))\r
\n" ); document.write( "\n" ); document.write( "I have a solution set of{-4,3} but the answer key shows the answer as {4}
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Algebra.Com's Answer #608944 by macston(5194) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( " $\"x%2F%28x-3%29+%2B+4%2F%28x%2B5%29=8x%2F%28%28x-3%29%28x%2B5%29%29\"$ Multiply each side by (x-3).
\n" ); document.write( " $\"x%2B%284%28x-3%29%29%2F%28x%2B5%29=%288x%29%2F%28x%2B5%29\"$ Multiply each side by (x+5).
\n" ); document.write( " $\"%28x%29%28x%2B5%29%2B%284%29%28x-3%29=8x\"$
\n" ); document.write( " $\"x%5E2%2B5x%2B4x-12=8x\"$ Subtract 8x from each side.
\n" ); document.write( " $\"x%5E2%2Bx-12=0\"$
\n" ); document.write( " $\"%28x%2B4%29%28x-3%29=0\"$
\n" ); document.write( " $\"x%2B4=0\"$ $\"OR\"$ $\"x-3=0\"$
\n" ); document.write( " $\"x=-4\"$ $\"OR\"$ $\"x=3\"$
\n" ); document.write( "From the domain of the original equation, we know xdoes not equal 3 or -5
\n" ); document.write( "(that would cause division by zero),so we are left with:
\n" ); document.write( "ANSWER: x=-4
\n" ); document.write( "You can check by putting the value in the original equation:
\n" ); document.write( "Negative 4 works, positive four does not,
\n" ); document.write( "so there is an error in your book.
\n" ); document.write( ".
\n" ); document.write( "CHECK:
\n" ); document.write( "For x=4:
\n" ); document.write( ".
\n" ); document.write( " $\"x%2F%28x-3%29+%2B+4%2F%28x%2B5%29=8x%2F%28%28x-3%29%28x%2B5%29%29\"$
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\n" ); document.write( " $\"4%2F%284-3%29%2B4%2F%284%2B5%29=%288%284%29%29%2F%28%284-3%29%284%2B5%29%29\"$
\n" ); document.write( ".
\n" ); document.write( " $\"4%2F1%2B4%2F9=32%2F9\"$
\n" ); document.write( " $\"36%2F9%2B4%2F9=32%2F9\"$
\n" ); document.write( " $\"40%2F9=32%2F9\"$ False, so 4 is NOT a solution.
\n" ); document.write( ".
\n" ); document.write( "For x=-4:
\n" ); document.write( " $\"x%2F%28x-3%29+%2B+4%2F%28x%2B5%29=8x%2F%28%28x-3%29%28x%2B5%29%29\"$
\n" ); document.write( " $\"-4%2F%28-4-3%29%2B4%2F%28-4%2B5%29=%288%28-4%29%29%2F%28%28-4-3%29%28-4%2B5%29%29\"$
\n" ); document.write( " $\"%28-4%2F-7%29%2B4=%28-32%2F-7%29\"$
\n" ); document.write( " $\"4%2F7%29%2B%2828%2F7%29=32%2F7\"$
\n" ); document.write( " $\"32%2F7=32%2F7\"$ True, -4 IS our solution.
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