document.write( "Question 327069: I need to simplify the complex fraction and reduce to lowest terms.\r
\n" ); document.write( "\n" ); document.write( "ab+b^2
\n" ); document.write( "------
\n" ); document.write( "4ab^5
\n" ); document.write( "------
\n" ); document.write( "a+b
\n" ); document.write( "------
\n" ); document.write( "6a^2b^4
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #234228 by jessica43(140)\"\" \"About 
You can put this solution on YOUR website!
((ab+b^2)/(4ab^5))/((a+b)/(6a^2b^4))
\n" ); document.write( "Dividing by a fraction is the same as multiplying by the fraction's reciprocal (the reciprocal is just the fraction flipped upside-down). So:
\n" ); document.write( "((ab+b^2)/(4ab^5))/((a+b)/(6a^2b^4))=
\n" ); document.write( "((ab+b^2)/(4ab^5))*((6a^2b^4)/(a+b))=
\n" ); document.write( "((ab+b^2)*(6a^2b^4))/((4ab^5)*(a+b))
\n" ); document.write( "Now you need to see if you can cancel anything in the numberator and the denominator. If you factor the numerator (factor out a b from the first term), you can cancel out the (a+b)from the num and denom:
\n" ); document.write( "((ab+b^2)*(6a^2b^4))/((4ab^5)*(a+b))=
\n" ); document.write( "((b)(a+b)*(6a^2b^4))/((4ab^5)*(a+b))=
\n" ); document.write( "((b)*(6a^2b^4))/(4ab^5)=
\n" ); document.write( "Now multiply out the numerator to see if that will enable you to cancel anything else out:
\n" ); document.write( "((b)*(6a^2b^4))/(4ab^5)=
\n" ); document.write( "(6a^2b^5)/(4ab^5)
\n" ); document.write( "Now cancel the b^5:
\n" ); document.write( "(6a^2)/(4a)
\n" ); document.write( "This can also be written as (6aa)/(4a), so you can cancel an a:
\n" ); document.write( "(6a)/4
\n" ); document.write( "This can be reduced to
\n" ); document.write( "3a/2
\n" ); document.write( "So your simplifed fraction is 3a/2.
\n" ); document.write( "
\n" );