document.write( "Question 178228: Solve: 3 over 2x-3 minus 5 over x = 1 \n" ); document.write( "

Algebra.Com's Answer #133200 by nerdybill(7384) $\"\"$ $\"About$

You can put this solution on YOUR website!
3 over 2x-3 minus 5 over x = 1
\n" ); document.write( " $\"3%2F%282x-3%29+-+5%2Fx+=+1\"$
\n" ); document.write( "Start by multiplying both sides by a common denominator x(2x-3):
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\n" ); document.write( " $\"x%282x-3%29%283%2F%282x-3%29+-+5%2Fx%29+=+x%282x-3%29%281%29\"$
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\n" ); document.write( "This results in:
\n" ); document.write( " $\"3x+-+5%282x-3%29+=+x%282x-3%29\"$
\n" ); document.write( " $\"3x+-+10x+%2B+15+=+2x%5E2+-+3x+\"$
\n" ); document.write( " $\"-7x+%2B+15+=+2x%5E2+-+3x+\"$
\n" ); document.write( " $\"15+=+2x%5E2+%2B+4x+\"$
\n" ); document.write( " $\"0+=+2x%5E2+%2B+4x+-+15\"$
\n" ); document.write( "Solve for 'x' using the quadratic equation yields:
\n" ); document.write( "x = {1.915, -3.915}
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\n" ); document.write( "Below are the details of the quadratic:
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"2x%5E2%2B4x%2B-15+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%284%29%5E2-4%2A2%2A-15=136\"$ .
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\n" ); document.write( " Discriminant d=136 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28-4%2B-sqrt%28+136+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%284%29%2Bsqrt%28+136+%29%29%2F2%5C2+=+1.91547594742265\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%284%29-sqrt%28+136+%29%29%2F2%5C2+=+-3.91547594742265\"$
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\n" ); document.write( " Quadratic expression $\"2x%5E2%2B4x%2B-15\"$ can be factored:
\n" ); document.write( " $\"2x%5E2%2B4x%2B-15+=+2%28x-1.91547594742265%29%2A%28x--3.91547594742265%29\"$
\n" ); document.write( " Again, the answer is: 1.91547594742265, -3.91547594742265.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-15+%29\"$

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