document.write( "Question 136439This question is from textbook
\n" ); document.write( ": y/y-4 -6/y+7= y^2/y^2+3y-28 \n" ); document.write( "
Algebra.Com's Answer #99953 by algebrapro18(249)\"\" \"About 
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\"%28y%2F%28y-4%29%29+-%286%2F%28y%2B7%29%29=+%28y%5E2%2F%28y%5E2%2B3y-28%29%29\"
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\n" ); document.write( "\n" ); document.write( "First off we need to find a common denominator. To do this I suggest factoring the denominator on the right hand side and seeing what you get.
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\n" ); document.write( "\n" ); document.write( "y^2+3y-28
\n" ); document.write( "we need factors that add to 3 but multiply to -28
\n" ); document.write( "28:
\n" ); document.write( "1,28
\n" ); document.write( "2,14
\n" ); document.write( "-4,7
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\n" ); document.write( "\n" ); document.write( "-4+7 = 3 and -4(7)=-28 so we know that
\n" ); document.write( "y^2+3y-28
\n" ); document.write( "=(y-4)(y+7)
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\n" ); document.write( "\n" ); document.write( "Now that the denominator is factored it is very easy to see that our common denominator is going to be (y-4)(y+7) because every rational expression has either a y-4 or a y+7 in it. So multiply the top of the left hand side and right hand side by (y-4)(y+7) and solve the remaining equation.
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\n" ); document.write( "\n" ); document.write( "\"%28y%2F%28y-4%29%29+-%286%2F%28y%2B7%29%29=+%28y%5E2%2F%28%28y-4%29%28y%2B7%29%29%29\" --> Multiply by your common denominator.
\n" ); document.write( " --> cancel like terms
\n" ); document.write( "y(y+7)-6(y-4)= y^2 --> Distribute
\n" ); document.write( "y^2+7y-6y+24 = y^2 --> Collect Like Terms
\n" ); document.write( "y^2-y^2+7y-6y+24 = 0 --> Simplify
\n" ); document.write( "y+24 = 0 --> Subtract 24 from both sides(solve for y)
\n" ); document.write( "y = -24 \n" ); document.write( "
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