document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346936>Question 346936</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^2-16/x^2-2x-8*x=2/x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248068 by </B><A HREF=/tutors/aboutme.mpl?userid=haileytucki><B>haileytucki(390)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=haileytucki><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=haileytucki><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=248068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x^(2)-16)/(x^(2)-2x-8)*x=(2)/(x^(2))\r<BR>\n" );
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document.write( "ALL ~ signs stand for the square root of and the / signs mean +-\r<BR>\n" );
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document.write( "The binomial can be factored using the difference of squares formula, because both terms are perfect squares.  The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).<BR>\n" );
document.write( "((x-4)(x+4))/(x^(2)-2x-8)*x=(2)/(x^(2))\r<BR>\n" );
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document.write( "In this problem 2*-4=-8 and 2-4=-2, so insert 2 as the right hand term of one factor and -4 as the right-hand term of the other factor.<BR>\n" );
document.write( "((x-4)(x+4))/((x+2)(x-4))*x=(2)/(x^(2))\r<BR>\n" );
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document.write( "Reduce the expression by canceling out the common factor of (x-4) from the numerator and denominator.<BR>\n" );
document.write( "(<X>(x-4)<x>(x+4))/((x+2)<X>(x-4)<x>)*x=(2)/(x^(2))\r<BR>\n" );
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document.write( "Reduce the expression by canceling out the common factor of (x-4) from the numerator and denominator.<BR>\n" );
document.write( "(x+4)/(x+2)*x=(2)/(x^(2))\r<BR>\n" );
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document.write( "Multiply the rational expressions to get (x(x+4))/((x+2)).<BR>\n" );
document.write( "(x(x+4))/(x+2)=(2)/(x^(2))\r<BR>\n" );
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document.write( "Since there is one rational expression on each side of the equation, this can be solved as a ratio.  For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.<BR>\n" );
document.write( "x(x+4)*x^(2)=2*(x+2)\r<BR>\n" );
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document.write( "Multiply x by x^(2) to get x^(3).<BR>\n" );
document.write( "x^(3)(x+4)=2*(x+2)\r<BR>\n" );
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document.write( "Multiply 2 by each term inside the parentheses.<BR>\n" );
document.write( "x^(3)(x+4)=2x+4\r<BR>\n" );
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document.write( "Multiply x^(3) by each term inside the parentheses.<BR>\n" );
document.write( "x^(4)+4x^(3)=2x+4\r<BR>\n" );
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document.write( "Since 2x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 2x from both sides.<BR>\n" );
document.write( "x^(4)+4x^(3)-2x=4\r<BR>\n" );
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document.write( "To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.<BR>\n" );
document.write( "x^(4)+4x^(3)-2x-4=0\r<BR>\n" );
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document.write( "Use the quadratic formula to find the solutions.  In this case, the values are a=1, b=4, and c=-2-4.<BR>\n" );
document.write( "x=(-b\~(b^(2)-4ac))/(2a) where ax^(2)+bx+c=0\r<BR>\n" );
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document.write( "Use the standard form of the equation to find a, b, and c for this quadratic.<BR>\n" );
document.write( "a=1, b=4, and c=-2-4\r<BR>\n" );
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document.write( "Substitute in the values of a=1, b=4, and c=-2-4.<BR>\n" );
document.write( "x=(-4\~((4)^(2)-4(1)(-2-4)))/(2(1))\r<BR>\n" );
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document.write( "Simplify the section inside the radical.<BR>\n" );
document.write( "x=(-4\2~(10))/(2(1))\r<BR>\n" );
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document.write( "Simplify the denominator of the quadratic formula.<BR>\n" );
document.write( "x=(-4\2~(10))/(2)\r<BR>\n" );
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document.write( "First, solve the + portion of \.<BR>\n" );
document.write( "x=(-4+2~(10))/(2)\r<BR>\n" );
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document.write( "Simplify the expression to solve for the + portion of the \.<BR>\n" );
document.write( "x=-2+~(10)\r<BR>\n" );
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document.write( "Next, solve the - portion of \.<BR>\n" );
document.write( "x=(-4-2~(10))/(2)\r<BR>\n" );
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document.write( "Simplify the expression to solve for the - portion of the \.<BR>\n" );
document.write( "x=-2-~(10)\r<BR>\n" );
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document.write( "The final answer is the combination of both solutions.<BR>\n" );
document.write( "x=-2+~(10),-2-~(10)\r<BR>\n" );
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document.write( "Verify each of the first set of solutions by substituting them into the original equation and solving.  In this case, none of the solutions are valid.<BR>\n" );
document.write( "No Solution </SPAN>\n" );
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