document.write( "Question 1086726: (3x/2x-1)-(4x/3x+1)=(18/6x^2-x-1)\r
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Algebra.Com's Answer #700957 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
I believe that you mean
\n" ); document.write( "\"3x%2F%282x-1%29-4x%2F%283x%2B1%29\"\"%22=%22\"\"18%2F%286x%5E2-x-1%29\" ,
\n" ); document.write( "and that is the problem I am going to try rto solve.
\n" ); document.write( "\"3x%2F%282x-1%29-4x%2F%283x%2B1%29\"\"%22=%22\"\"18%2F%286x%5E2-x-1%29\"
\n" ); document.write( "\"3x%2F%282x-1%29-4x%2F%283x%2B1%29\"\"%22=%22\"\"18%2F%28%283x%2B1%29%282x-1%29%29\"
\n" ); document.write( "Multiplying both sides of the equation times \"%283x%2B1%29%282x-1%29\" , we get
\n" ); document.write( "\"3x%283x%2B1%29-4x%282x-1%29=18\"
\n" ); document.write( "\"9x%5E2%2B3x-8x%5E2%2B4x=18\"
\n" ); document.write( "\"3x%283x%2B1%29-4x%282x-1%29=18\"
\n" ); document.write( "\"x%5E2%2B7x=18\"
\n" ); document.write( "\"x%5E2%2B7x-18=0\"
\n" ); document.write( "\"%28x-2%29%28x%2B9%29=0\"
\n" ); document.write( "So, either \"x-2=0\" <--> \"highlight%28x=2%29\" ,
\n" ); document.write( "or \"x%2B9=0\" <--> \"highlight%28x=-9%29\" .
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\n" ); document.write( "NOTE:
\n" ); document.write( "A group of conventions often called \"order of operations\"
\n" ); document.write( "is taught (but not always clearly explained) in beginning algebra.
\n" ); document.write( "We use a lot of conventions in math (as in any language).
\n" ); document.write( "The symbols for numbers and operations are the first you were taught.
\n" ); document.write( "After that, in elementary school,
\n" ); document.write( "you could show solutions to simple problems one step at a time
\n" ); document.write( "(one mathematical operation at a time).
\n" ); document.write( "That is like being able to talk a single word at a time,
\n" ); document.write( "before we speak in whole sentences.
\n" ); document.write( "It is a good first step, but hopefully we grow to be able to do more.
\n" ); document.write( "After learning the basics, you want to be able to talk/write a whole sentence,
\n" ); document.write( "and to be able to communicate efficiently,
\n" ); document.write( "we had to agree on some conventions.
\n" ); document.write( "We agreed on what \"man bites dog\" and what \"dog bites man\" mean.
\n" ); document.write( "We also agreed that the expression for the total cost in dollars at the pharmacy of
\n" ); document.write( "5 cans of tuna, 2 bags of potato chips, 3 pack of batteries and 1 tube of toothpaste
\n" ); document.write( "would be written as
\n" ); document.write( "5 X 1 + 2 X 2 + 3 X 7 + 4
\n" ); document.write( "rather than
\n" ); document.write( "(5 X 1) + (2 X 2) + (3 X 7) + 4 .
\n" ); document.write( "That agreement saves brackets, ink, and handwriting work.
\n" ); document.write( "By convention,
\n" ); document.write( "whatever is between plus and minus signs is calculated first,
\n" ); document.write( "unless parentheses are involved.
\n" ); document.write( "Parentheses are useful when we need them.
\n" ); document.write( "Often undeclared (or not emphasized enough) conventions
\n" ); document.write( "give other symbols similar effort-saving usefulness.
\n" ); document.write( "Those horizontal lines we use to separate expressions used as numerator and denominator
\n" ); document.write( "are agreed to includes invisible parentheses around numerator and denominator,
\n" ); document.write( "so we can save ink and effort when we write rational expressions on two lines.
\n" ); document.write( "That agreement was a great invention.
\n" ); document.write( "However, sometimes we cannot write double-decker expressions,
\n" ); document.write( "and then we need to wrap those numerators and denominators in brackets.
\n" ); document.write( "The expressions \"3x%2F%282x-1%29-4x%2F%283x%2B1%29\" and \"18%2F%286x%5E2-x-1%29\", written in one line
\n" ); document.write( "(as you would enter numbers in a calculator when evaluating those expressions),
\n" ); document.write( "should be written with strategically placed parentheses indicating what parts to calculate first,
\n" ); document.write( "as in 3x/(2x-1)-4x/(3x+1) and 18/(6x^2-x-1) .
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