document.write( "Question 250219: This is the third time I have asked a question but no solution to any problems.
\n" ); document.write( "I do not understand how to Simplify completely
\n" ); document.write( "-7xy^2 over 28x^2y
\n" ); document.write( "x-2 over 8x^2-32\r
\n" ); document.write( "\n" ); document.write( "Find the LCD
\n" ); document.write( "(5) (7)/(x-6'x^2-12x+36)
\n" ); document.write( "5 -2 over 7ab^5' 7a^3b^3 \n" ); document.write( "
Algebra.Com's Answer #182163 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
You will probably have better success getting tutors to help if:
  • there is one problem in each posting. (Maybe two if they are closely related types of problems.)
  • the problem is posted coherently. Please
    • proofread your posting before submitting it.
    • use parentheses generously, especially around multi-term
      • numerators
      • denominators
      • exponents
      • arguments to functions (for example: log(3x+4))
      • radicands (expressions within radicals) (for example: sqrt(x^2-4x + 4))

    \n" ); document.write( "The first two problems are to simplify fractions. In other words we are going to reduce the fractions if we can. And how do youreduce a fraction? Answer: You cancel factors that are common to the numerator and denominator. So to reduce a fraction we need to know the factors of the numerator and denominator. In other words, we need to factor the numerator and denominator, hoping to find factors that are in common.

    \n" ); document.write( "\"-7xy%5E2%2F28x%5E2y\"
    \n" ); document.write( "Factoring the top and bottom we get:
    \n" ); document.write( "\"%28-1%29%2A7%2Ax%2Ay%2Ay%2F7%2A4%2Ax%2Ax%2Ay\"
    \n" ); document.write( "We can see the common factors: 7, x and y. We can cancel them out:
    \n" ); document.write( "
    \n" ); document.write( "leaving:
    \n" ); document.write( "\"%28-1%29%2Ay%2F4%2Ax\"
    \n" ); document.write( "which simplifies to
    \n" ); document.write( "\"%28-y%29%2F4x\"

    \n" ); document.write( "\"%28x-2%29%2F%288x%5E2-32%29\"
    \n" ); document.write( "Factoring the top and bottom. Only a 1 can be factored out in the numerator. An 8 can be factored out in the denominator:
    \n" ); document.write( "\"%281%2A%28x-2%29%29%2F%288%28x%5E2-4%29%29\"
    \n" ); document.write( "When factoring you should always factor until no more factoring can be done (or until you get the factors you want). The \"x%5E2-4\" factor in the denominator is a difference of squares, \"x%5E2+-+2%5E2\". So it will factor according to the difference of squares pattern, \"a%5E2+-+b%5E2+=+%28a%2Bb%29%28a-b%29\". Using this pattern on \"x%5E2-4\" we get:
    \n" ); document.write( "\"%281%2A%28x-2%29%29%2F%288%28x%2B2%29%28x-2%29%29\"
    \n" ); document.write( "And only by factoring completely do we find a common factor to cancel: (x-2)
    \n" ); document.write( "\"%281%2Across%28%28x-2%29%29%29%2F%288%28x%2B2%29cross%28%28x-2%29%29%29\"
    \n" ); document.write( "leaving:
    \n" ); document.write( "\"1%2F%288%28x%2B2%29%29\"
    \n" ); document.write( "Now that we have finished reducing the fraction we can simplify the denominator (i.e multiply it out):
    \n" ); document.write( "\"1%2F%288x%2B16%29\"

    \n" ); document.write( "The rest of your posting after \"Find the LCD\" makes no sense at all.\r
    \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );