document.write( "Question 299158: Solve by the LCM method:\r
\n" ); document.write( "\n" ); document.write( " $\"6%2F%28y%2B3%29%2B+2%2Fy+=%285y-3%29%2F%28y%5E2-9%29\"$ \r
\n" ); document.write( "\n" ); document.write( "I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this. Once I have the LCD, I believe I will be able to solve it. Thank you in advance for your help. \n" ); document.write( "

Algebra.Com's Answer #854280 by ikleyn(53875) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Solve by the LCM method:\r
\n" ); document.write( "\n" ); document.write( " $\"6%2F%28y%2B3%29\"$ + $\"2%2Fy\"$ = $\"%285y-3%29%2F%28y%5E2-9%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this.
\n" ); document.write( "Once I have the LCD, I believe I will be able to solve it. Thank you in advance for your help.
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\n" ); document.write( "\n" ); document.write( " The solution in the post by @mananth is incorrect.\r
\n" ); document.write( "\n" ); document.write( " I came to bring a correct solution.\r
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document.write( "LCM (the Least Common Multiple) is y*(y^2-9) = y*((-3)*(y+3).\r\n" );
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document.write( "So, we multiply both sides of the given equation by this expression y*(y-3)*(y+3).\r\n" );
document.write( "We get\r\n" );
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document.write( "    6y*(y-3) + 2(Y^2-9) = (5y-3)y,\r\n" );
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document.write( "    6y^2 - 18y + 2y^2 - 18 = 5y^2 -3y,\r\n" );
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document.write( "    3y^2 - 15y - 18 = 0,\r\n" );
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document.write( "    y^2 - 5y - 6 = 0,\r\n" );
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document.write( "    (y-6)*(y+1) = 0.\r\n" );
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document.write( "The roots are  y = 6  and/or  y = -1.\r\n" );
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document.write( "ANSWER.  The solutions for the given equation are  y= 6  and/or  y = -1.\r\n" );
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document.write( "To  ,  I used a free of charge plotting tool at web-site  http:\\www.desmos.com/calculator/\r\n" );
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document.write( "I printed the formulas for the left side and right side functions and got two plots.\r\n" );
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document.write( "They have exactly two intersection points at y = 6  and  y = -1  , confirming my solution.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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