document.write( "Question 75030This question is from textbook
\n" ); document.write( ": Please help me solve this equation and check my solution. \"+18%2F%28x-3%29+=+x%2F3+\"
\n" ); document.write( " Sorry I didn't know how to put the line under the numerator!!!
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Algebra.Com's Answer #53915 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
To make a fraction of \"18%2F%28x-3%29\" just place 18/(x-3) in triple curly brackets.
\n" ); document.write( " \"+18%2F%28x-3%29+=+x%2F3+\" Start with the given problem
\n" ); document.write( " \"+%283%2F1%29%2818%2F%28x-3%29%29+=+%28x%2Fcross%283%29%29%28cross%283%29%2F1%29\"Multiply both sides by 3, this eliminates the denominator of the right side
\n" ); document.write( "\"cross%28x-3%29%2854%2Fcross%28x-3%29%29=x%28x-3%29\"Multiply both sides by (x-3), this eliminates the denominator of the left side
\n" ); document.write( "So we're left with this:
\n" ); document.write( "\"54=x%28x-3%29\"
\n" ); document.write( "\"54=x%5E2-3x%29\"Distribute the x
\n" ); document.write( "\"0=x%5E2-3x-54%29\"Subtract 54 from both sides
\n" ); document.write( "\"0=%28x-9%29%28x%2B6%29\"Factor the right side
\n" ); document.write( "\"x-9=0\"
\n" ); document.write( "\"x=9\"There's one answer
\n" ); document.write( "\"x%2B6=0\"
\n" ); document.write( "\"x=-6\"There's the other answer
\n" ); document.write( "So the solution is x=9 and x=-6
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\n" ); document.write( "Check:
\n" ); document.write( " \"+18%2F%28x-3%29+=+x%2F3+\"Plug in x=9
\n" ); document.write( "\"+18%2F%289-3%29+=+9%2F3+\"
\n" ); document.write( "\"+18%2F6+=+3+\"
\n" ); document.write( "\"+3=+3+\"works
\n" ); document.write( "\"+18%2F%28x-3%29+=+x%2F3+\"Plug in x=-6
\n" ); document.write( "\"+18%2F%28%28-6%29-3%29+=+-6%2F3+\"
\n" ); document.write( "\"+18%2F%28-9%29+=+-2+\"
\n" ); document.write( "\"+-2=+-2+\"works\r
\n" ); document.write( "\n" ); document.write( "Here's another way to solve it:
\n" ); document.write( "When you have the quadratic \"0=x%5E2-3x-54%29\", plug the coefficients into the quadratic formula:
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-3x%2B-54+=+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=%28-3%29%5E2-4%2A1%2A-54=225\".
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\n" ); document.write( " Discriminant d=225 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--3%2B-sqrt%28+225+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+225+%29%29%2F2%5C1+=+9\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-3%29-sqrt%28+225+%29%29%2F2%5C1+=+-6\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-3x%2B-54\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-3x%2B-54+=+1%28x-9%29%2A%28x--6%29\"
\n" ); document.write( " Again, the answer is: 9, -6.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-3%2Ax%2B-54+%29\"

\n" ); document.write( "\n" ); document.write( "And you see the same answer, but it's just another way to get there. \n" ); document.write( "

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