document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82035>Question 82035</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0812387511/algebrahomeworkh>Algebra 1 an integraded approach</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> how do I simplify this and give restrictions?\r<BR>\n" );
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document.write( "2x^2 + 7x -15<BR>\n" );
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document.write( "x^2 + x - 20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58765 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=58765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you need help with factoring take a look at this <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/quadratic-factoring.solver\"> solver</a>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2+%2B+7x+-15%29%2F%28x%5E2+%2B+x+-+20%29 ALIGN=MIDDLE  ALT=\"%282x%5E2+%2B+7x+-15%29%2F%28x%5E2+%2B+x+-+20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given problem\r<BR>\n" );
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document.write( "Factor the numerator\r<BR>\n" );
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document.write( "ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.\n" );
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document.write( " <TR><TD >Error occurred executing solver 'quadratic_factoring' .</TD></TR>\n" );
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document.write( "Factor the denominator\r<BR>\n" );
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document.write( "ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'quadratic_factoring'.\n" );
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document.write( " <TR><TD >Error occurred executing solver 'quadratic_factoring' .</TD></TR>\n" );
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document.write( "So after factoring we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x-3%29%28x%2B5%29%29%2F%28%28x-4%29%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"%28%282x-3%29%28x%2B5%29%29%2F%28%28x-4%29%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x-3%29cross%28%28x%2B5%29%29%29%2F%28%28x-4%29cross%28%28x%2B5%29%29%29 ALIGN=MIDDLE  ALT=\"%28%282x-3%29cross%28%28x%2B5%29%29%29%2F%28%28x-4%29cross%28%28x%2B5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel like terms \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. This is the simplified form.\r<BR>\n" );
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document.write( "Now in order for the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x-4%29 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "to be equivalent to \r<BR>\n" );
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document.write( "We need to find the restrictions. So we need to set the denominators equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4=0 ALIGN=MIDDLE  ALT=\"x-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5=0 ALIGN=MIDDLE  ALT=\"x%2B5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5 ALIGN=MIDDLE  ALT=\"x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the restrictions are that x cannot equal 4 or -5. Notice if we plug in x=4 into the original equation we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%284%29%5E2+%2B+7%284%29+-15%29%2F%284%5E2+%2B+4+-+20%29=45%2F0 ALIGN=MIDDLE  ALT=\"%282%284%29%5E2+%2B+7%284%29+-15%29%2F%284%5E2+%2B+4+-+20%29=45%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is not possible\r<BR>\n" );
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document.write( "the same applies to x=-5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28-5%29%5E2+%2B+7%28-5%29+-15%29%2F%28%28-5%29%5E2+-5+-+20%29=0%2F0 ALIGN=MIDDLE  ALT=\"%282%28-5%29%5E2+%2B+7%28-5%29+-15%29%2F%28%28-5%29%5E2+-5+-+20%29=0%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is also not possible </SPAN>\n" );
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