document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76095>Question 76095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need the solution\r<BR>\n" );
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document.write( "(5/y-3) - (30 /y^2-9) = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54632 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54632\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28y-3%29+-+30+%2F%28y%5E2-9%29+=+1 ALIGN=MIDDLE  ALT=\"5%2F%28y-3%29+-+30+%2F%28y%5E2-9%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-9 ALIGN=MIDDLE  ALT=\"y%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the difference of two squares. The rule that applies to<BR>\n" );
document.write( "factoring the difference between two squares is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2+=+%28a+%2B+b%29%2A%28a+-+b%29 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2+=+%28a+%2B+b%29%2A%28a+-+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Applying this rule to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+9 ALIGN=MIDDLE  ALT=\"y%5E2+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+9=+%28y+%2B+3%29%2A%28y+-+3%29 ALIGN=MIDDLE  ALT=\"y%5E2+-+9=+%28y+%2B+3%29%2A%28y+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substituting this into the equation changes the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F%28y-3%29+-+30%2F%28%28y%2B3%29%2A%28y-3%29%29+=+1 ALIGN=MIDDLE  ALT=\"5%2F%28y-3%29+-+30%2F%28%28y%2B3%29%2A%28y-3%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can get all the terms over the common denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+%2B+3%29%2A%28y+-+3%29 ALIGN=MIDDLE  ALT=\"%28y+%2B+3%29%2A%28y+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Multiply the<BR>\n" );
document.write( "first term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B3%29%2F%28y%2B3%29 ALIGN=MIDDLE  ALT=\"%28y%2B3%29%2F%28y%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the same as multiplying the first term by 1 because<BR>\n" );
document.write( "the numerator of this multiplier is the same as the denominator.  When you do this <BR>\n" );
document.write( "multiplication the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28y%2B3%29%2F%28%28y%2B3%29%2A%28y-3%29%29+-+30%2F%28%28y%2B3%29%2A%28y-3%29%29+=+1 ALIGN=MIDDLE  ALT=\"5%28y%2B3%29%2F%28%28y%2B3%29%2A%28y-3%29%29+-+30%2F%28%28y%2B3%29%2A%28y-3%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then multiply the 1 on the right side by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2B3%29%2A%28y-3%29%29%2F%28%28y%2B3%29%2A%28y-3%29%29 ALIGN=MIDDLE  ALT=\"%28%28y%2B3%29%2A%28y-3%29%29%2F%28%28y%2B3%29%2A%28y-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This multiplication<BR>\n" );
document.write( "results in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28y%2B3%29%2F%28%28y%2B3%29%2A%28y-3%29%29+-+30%2F%28%28y%2B3%29%2A%28y-3%29%29+=+%28%28y%2B3%29%2A%28y-3%29%29%2F%28%28y%2B3%29%2A%28y-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now you can multiply the entire equation (both sides, all terms) by the common denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28y%2B3%29%2A%28y-3%29%29 ALIGN=MIDDLE  ALT=\"+%28%28y%2B3%29%2A%28y-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and after that multiplication you are left with only the numerators<BR>\n" );
document.write( "of all the terms in the equation.  The result is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28y%2B3%29+-+30+=+%28y+%2B+3%29%2A%28y+-+3%29 ALIGN=MIDDLE  ALT=\"5%2A%28y%2B3%29+-+30+=+%28y+%2B+3%29%2A%28y+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply where called for and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+%2B+15+-+30+=+y%5E2+-+9 ALIGN=MIDDLE  ALT=\"5y+%2B+15+-+30+=+y%5E2+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-9 ALIGN=MIDDLE  ALT=\"y%5E2-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y+%2B+15+-+30+-+y%5E2+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"5y+%2B+15+-+30+-+y%5E2+%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rearrange terms in descending powers of y:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%5E2+%2B+5y+%2B+15+-+30+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"-y%5E2+%2B+5y+%2B+15+-+30+%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the constants:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%5E2+%2B+5y+-+6+=+0 ALIGN=MIDDLE  ALT=\"-y%5E2+%2B+5y+-+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply the entire equation (both sides and all terms) by -1 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+5y+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+-+5y+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This factors to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-3%29%2A%28y-2%29+=+0 ALIGN=MIDDLE  ALT=\"%28y-3%29%2A%28y-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If either of the factors equals zero, then the equation is true because a multiplication<BR>\n" );
document.write( "by zero on the left side, makes the entire left side equal to the zero on the right side.<BR>\n" );
document.write( "Find the solutions for y by setting each of the factors equal to zero and solving for<BR>\n" );
document.write( "y ...<BR>\n" );
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document.write( "y - 2 = 0 <---- add 2 to both sides<BR>\n" );
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document.write( "y = +2  <--- one answer for y<BR>\n" );
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document.write( "y - 3 = 0 <--- add 3 to both sides<BR>\n" );
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document.write( "y = +3 <--- the second answer for y<BR>\n" );
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document.write( "But the second answer [y = +3] is not permitted because this would cause a division by<BR>\n" );
document.write( "zero in the second term of the original equation ... the denominator of the second term<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+-+9 ALIGN=MIDDLE  ALT=\"y%5E2+-+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B3%29%2A%28y-3%29 ALIGN=MIDDLE  ALT=\"%28y%2B3%29%2A%28y-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and if y is allowed to equal<BR>\n" );
document.write( "+3 then one of the factors in the denominator is zero ... and division by zero is not <BR>\n" );
document.write( "permitted.<BR>\n" );
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document.write( "So there you are ... the answer to the equation is y = +2.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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