document.write( "Question 105218: 1/x-4 +x/x-5 +1/x^2-9x+20=0 I have to solve for x I have the LCD to be(x-4)(x-5) I multiplied the numerator times the LCD and got (x-5)+x(x-4)+1=0. Next I got x-5+x^2-4x+1=0. I combined my like terms and got -3x-4+x^=0. The x ^2 keeps throwing me off because I don't know what to do with it. Please show me what to do. \n" ); document.write( "
Algebra.Com's Answer #76591 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'm going to start where you left off\r
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\n" ); document.write( "\n" ); document.write( "\"-3x-4%2Bx%5E2=0\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-3x-4=0\" Rearrange the terms\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"x%5E2-3%2Ax-4=0\" ( notice \"a=1\", \"b=-3\", and \"c=-4\")
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\n" ); document.write( " \"x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29\" Plug in a=1, b=-3, and c=-4
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-4+%29%29%2F%282%2A1%29\" Negate -3 to get 3
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9-4%2A1%2A-4+%29%29%2F%282%2A1%29\" Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because \"%28-3%29%5E2=-3%2A-3=9\".)
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%2A1%29\" Multiply \"-4%2A-4%2A1\" to get \"16\"
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\n" ); document.write( " \"x+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%283+%2B-+5%29%2F%282%2A1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%283+%2B-+5%29%2F2\" Multiply 2 and 1 to get 2
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%283+%2B+5%29%2F2\" or \"x+=+%283+-+5%29%2F2\"
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\n" ); document.write( " Lets look at the first part:
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\n" ); document.write( " \"x=%283+%2B+5%29%2F2\"
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\n" ); document.write( " \"x=8%2F2\" Add the terms in the numerator
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\n" ); document.write( " \"x=4\" Divide
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\n" ); document.write( " So one answer is
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\n" ); document.write( " \"x=4\"
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\n" ); document.write( " Now lets look at the second part:
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\n" ); document.write( " \"x=%283+-+5%29%2F2\"
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\n" ); document.write( " \"x=-2%2F2\" Subtract the terms in the numerator
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\n" ); document.write( " \"x=-1\" Divide
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\n" ); document.write( " So another answer is
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\n" ); document.write( " \"x=-1\"
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\n" ); document.write( " So our solutions are:
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\n" ); document.write( " \"x=4\" or \"x=-1\"
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\n" ); document.write( "\n" ); document.write( "However, since \"x=4\" makes two terms of the original equation \"1%2F%28x-4%29+%2Bx%2F%28x-5%29+%2B1%2F%28x%5E2-9x%2B20%29=0\" have a denominator of zero, our only true solution is \"x=-1\"\r
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\n" ); document.write( "\n" ); document.write( "So our answer is \"x=-1\"\r
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