document.write( "Question 60652: How do I solve for z?\r
\n" ); document.write( "\n" ); document.write( "1/3z+15+4=8/z+5
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Algebra.Com's Answer #41774 by ankor@dixie-net.com(22740)\"\" \"About 
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How do I solve for z?
\n" ); document.write( "1/3z+15+4=8/z+5
\n" ); document.write( ":
\n" ); document.write( "Assume you mean:
\n" ); document.write( "\"1%2F%283z%2B15%29%2B4=8%2F%28z%2B5%29\"
\n" ); document.write( ":
\n" ); document.write( "Get rid of the denominators, mult eq by (3z+15)(z+5), resulting in:
\n" ); document.write( "(z+5) + 4(3z+15)(z+5) = 8(3z+15)
\n" ); document.write( ":
\n" ); document.write( "(z+5) + 4(3z^2 + 30z + 75) = 24z + 120
\n" ); document.write( ":
\n" ); document.write( "z + 5 + 12z^2 + 120z + 300 = 24z + 120
\n" ); document.write( ":
\n" ); document.write( "12z^2 + z + 120z - 24z + 5 + 300 - 120 = 0
\n" ); document.write( ":
\n" ); document.write( "12z^2 + 97z + 185 = 0
\n" ); document.write( ":
\n" ); document.write( "Use the quadratic formula. a=12; b=97; c=185
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "\"z+=+%28-97+%2B-+sqrt%2897%5E2-4%2A12%2A185+%29%29%2F%282%2A12%29+\"
\n" ); document.write( "\"z+=+%28-97+%2B-+sqrt%289409+-+8880%29%29%2F24\"
\n" ); document.write( "\"z+=+%28-97+%2B-+sqrt%28529%29%29%2F24\"
\n" ); document.write( "\"z+=+%28-97+%2B-+sqrt%28529%29%29%2F24\"
\n" ); document.write( "\"z+=+%28-97+%2B-+sqrt%28529%29%29%2F24\"
\n" ); document.write( "\"z+=+%28-97+%2B-+23%29%2F24\"
\n" ); document.write( "You can do the math here and see the solutions are:
\n" ); document.write( "z = -5 and z = -3.0833:
\n" ); document.write( ":
\n" ); document.write( "we have to be careful when there are unknowns in the denominator of the original equation to avoid dividing by 0.
\n" ); document.write( ":
\n" ); document.write( "Notice in the expression \"1%2F%283z%2B15%29\", if we substitute -5 for z we get a 0 in the denominator so that can't be a solution. The only solution is -3.0833
\n" ); document.write( "Try substituting -3.0833 for z in the original equation to see if equality is present. \n" ); document.write( "
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