document.write( "Question 151771: z+3/z+1=z^2+9z+20/z^2-z-2 look for the root \n" ); document.write( "
Algebra.Com's Answer #111572 by orca(409)\"\" \"About 
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Note that
\n" ); document.write( "\"z%5E2+%2B+9z+%2B+20+=+%28z+%2B+4%29%28z+%2B+5%29\"
\n" ); document.write( "\"z%5E2+-+z+-+2+=+%28z+-+2%29%28z+%2B+1%29\"\r
\n" ); document.write( "\n" ); document.write( "So the original equation becomes:
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\n" ); document.write( "Multiplying both sides by (z - 2)(z + 1), we have
\n" ); document.write( "(z + 3)(z - 2) = (z + 4)(z + 5)
\n" ); document.write( "Expanding, we have
\n" ); document.write( "\"z%5E2+%2B+z+-+6+=+z%5E2+%2B+9z+%2B+20\"
\n" ); document.write( "Simplifying, we have
\n" ); document.write( "-26 = 8z
\n" ); document.write( "z = -26/8 = -13/4\r
\n" ); document.write( "\n" ); document.write( "CHECK:
\n" ); document.write( "Left hand side = (-13/4) + 3)/(-13/4 + 1) = 1/9
\n" ); document.write( "Right hand side = [(-13/4)^2 + 9(-13/4) + 20]/[(-13/4)^2 - (-13/4) - 2]= 1/9
\n" ); document.write( "So z = -13/4 is the root of the original equation.
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