document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1076748>Question 1076748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the range of values of x for: [(4-4x^2)/(X^2+1)^2]>0<BR>\n" );
document.write( "If you look at the denominator, the denominator is always greater than zero because any nonzero number squared is a positive number.<BR>\n" );
document.write( "We should focus on the numerator.  Look at (4 - 4x^2) > 0.  We get here because we can multiply both sides of the inequality by (x^2 + 1)^2, cancelling it out from both sides of the inequality.<BR>\n" );
document.write( "Now solve for x in (4 - 4x^2) > 0<BR>\n" );
document.write( "4 > 4x^2<BR>\n" );
document.write( "1 > x^2<BR>\n" );
document.write( "sqrt(1) > sqrt(x^2)<BR>\n" );
document.write( "1 > |x|<BR>\n" );
document.write( "We see that by the definition of absolute value we get<BR>\n" );
document.write( "Either 1 > x OR 1 > -x<BR>\n" );
document.write( "1 > x OR -1 < x<BR>\n" );
document.write( "so  -1 < x < 1 is our solution. </SPAN>\n" );
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document.write( "If you look at the denominator, the denominator is always greater than zero because any nonzero number squared is a positive number.<BR>\n" );
document.write( "We should focus on the numerator.  Look at (4 - 4x^2) > 0.  We get here because we can multiply both sides of the inequality by (x^2 + 1)^2, cancelling it out from both sides of the inequality.<BR>\n" );
document.write( "Now solve for x in (4 - 4x^2) > 0<BR>\n" );
document.write( "4 > 4x^2<BR>\n" );
document.write( "1 > x^2<BR>\n" );
document.write( "sqrt(1) > sqrt(x^2)<BR>\n" );
document.write( "1 > |x|<BR>\n" );
document.write( "We see that by the definition of absolute value we get<BR>\n" );
document.write( "Either 1 > x OR 1 > -x<BR>\n" );
document.write( "1 > x OR -1 < x<BR>\n" );
document.write( "so  -1 < x < 1 is our solution. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );