document.write( "Question 128130: I am a homeschooling mom. I have come across these problems. I don't understand how it works. I want to be able to understand in order to teach my kid the right way. \r
\n" ); document.write( "\n" ); document.write( "Here are the problems in one 'sentence': ( if you see the dashes between these numbers - that is division. And..as for the # 3 and # 4 ...I have been unable to get the denominator to look the way it should... under the first combination it is divided by 2x; and the second combination, it is divded by an x.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "1.
\n" ); document.write( "3/2 + 3/x
\n" ); document.write( "--------- =
\n" ); document.write( " 2+4/x \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2.
\n" ); document.write( "(3/2+3/x)/(2+4/x)=\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3.
\n" ); document.write( "(3x+6)/(2x+4)
\n" ); document.write( "----- ---- =
\n" ); document.write( "2x x \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4.
\n" ); document.write( "3x+6 * 2x+4
\n" ); document.write( "---- ---- =
\n" ); document.write( "2x x \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "5.
\n" ); document.write( "\"+6x%5E2%2B24x%2B24+\"
\n" ); document.write( " -----------
\n" ); document.write( " \"+2x%5E2+\"
\n" ); document.write( "
\n" ); document.write( "I would very much appreciate your explanation and how you arrive to the answer..and please make it in layman's terms. Thanks.
\n" ); document.write( "

Algebra.Com's Answer #93930 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
1.
\n" ); document.write( "\"3%2F2\" + \"3%2Fx\"
\n" ); document.write( "-------
\n" ); document.write( "2 + \"4%2Fx\"
\n" ); document.write( ":
\n" ); document.write( "Put the fractions in the numerator & denominator over a single common denominator
\n" ); document.write( "\"%28%283x+%2B+2%283%29%29%29%2F%282x%29\"
\n" ); document.write( "----------
\n" ); document.write( "\"%28%282x+%2B+4%29%29%2Fx\"
\n" ); document.write( ":
\n" ); document.write( "\"%28%283x+%2B+6%29%29%2F%282x%29\"
\n" ); document.write( "----------
\n" ); document.write( "\"%28%282x+%2B+4%29%29%2Fx\"
\n" ); document.write( ":
\n" ); document.write( "Factor out 3 in the numerator & 2 in the denominator
\n" ); document.write( "\"%283%28x+%2B+2%29%29%2F%282x%29\"
\n" ); document.write( "----------
\n" ); document.write( "\"%282%28x+%2B+2%29%29%2Fx\"
\n" ); document.write( ";
\n" ); document.write( "Remember when you divide fractions, invert the dividing fraction and multiply
\n" ); document.write( "\"%283%28x%2B2%29%29%2F%282x%29\" * \"x%2F%282%28x%2B2%29%29\"
\n" ); document.write( ":
\n" ); document.write( "Cancel out (x+2) and x, leaving
\n" ); document.write( "\"3%2F2\" * \"1%2F2\" = \"3%2F4\"
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "2.
\n" ); document.write( "This is the same as the first one
\n" ); document.write( ":
\n" ); document.write( "3. This is similar to the first equation after we put it over common denominators
\n" ); document.write( "\"%28%283x%2B6%29%29%2F%282x%29\"
\n" ); document.write( "----------
\n" ); document.write( "\"%28%282x%2B4%29%29%2Fx\"
\n" ); document.write( ":
\n" ); document.write( "Factor out 3 in the numerator & 2 in the denominator
\n" ); document.write( "\"%283%28x+%2B+2%29%29%2F%282x%29\"
\n" ); document.write( "----------
\n" ); document.write( "\"%282%28x+%2B+2%29%29%2Fx\"
\n" ); document.write( ";
\n" ); document.write( "Remember when you divide fractions, invert the dividing fraction and multiply
\n" ); document.write( "\"%283%28x%2B2%29%29%2F%282x%29\" * \"x%2F%282%28x%2B2%29%29\"
\n" ); document.write( ":
\n" ); document.write( "Cancel out (x+2) and x, leaving
\n" ); document.write( "\"3%2F2\" * \"1%2F2\" = \"3%2F4\"
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "5.
\n" ); document.write( "6x^2+24x+24
\n" ); document.write( "-----------
\n" ); document.write( "2x^2
\n" ); document.write( ":
\n" ); document.write( "notice that you can factor out 6 in the numerator, then cancel 2 into 6
\n" ); document.write( "\"%286%28x%5E2+%2B+4x+%2B+4%29%29%2F%282x%5E2%29\" = \"%283%28x%5E2+%2B+4x+%2B+4%29%29%2F%28x%5E2%29\"
\n" ); document.write( ":
\n" ); document.write( "The numerator has a perfect square and can be factored to:
\n" ); document.write( "\"%283%28x%2B2%29%28x%2B2%29%29%2F%28x%5E2%29\" = \"%283%28x%2B2%29%5E2%29%2F%28x%5E2%29\" \r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );