Question 74436
{{{(2x+1)/(3x-1) - (x+4)/(x-2) }}}
The LCD is (3x-1)(x-2). So we multiply the terms to get to the LCD
{{{((x-2)/(x-2))((2x+1)/(3x-1)) - ((3x-1)/(3x-1))((x+4)/(x-2)) }}}Multiply both terms by a clever form of 1 to get to the LCD
{{{((x-2)(2x+1))/((3x-1)(x-2)) - ((3x-1)(x+4))/((3x-1)(x-2))}}}
{{{((x-2)(2x+1)-(3x-1)(x+4))/((3x-1)(x-2))}}}foil the two sets of parenthesis
{{{(2x^2-3x-2-3x^2-11x+4)/((3x-1)(x-2))}}}Add like terms
{{{(-x^2-14x+2)/((3x-1)(x-2))}}}There's your simplified answer
Note: you can graph these expressions and you'll see that they're equal

{{{graph( 300, 200, -6, 5, -10, 10, (-x^2-14x+2)/((3x-1)(x-2)))}}}Graph of {{{(-x^2-14x+2)/((3x-1)(x-2))}}}


{{{graph( 300, 200, -6, 5, -10, 10, (2x+1)/(3x-1) - (x+4)/(x-2))}}}Graph of {{{(2x+1)/(3x-1) - (x+4)/(x-2) }}}
So this shows that they are both equal.