Question 287802
<pre>
3/(x+1)   +4/(x-2)=(px+q)/(x+1)(x-2)   
What is the value of p and q?
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{{{3/(x + 1) + 4/(x - 2) = (px + q)/(x + 1)(x - 2)}}}   

Let's focus on the LEFT-SIDE of the equation
          {{{highlight(3/(x + 1) + 4/(x - 2)) = (px + q)/(x + 1)(x - 2)}}}  
{{{highlight((3(x - 2) + 4(x + 1))/(x + 1)(x - 2)) = (px + q)/(x + 1)(x - 2)}}} ---- Multiplying left-side by GCF (x + 1)(x - 2) 
        {{{highlight((3x - 6 + 4x + 4)/(x + 1)(x - 2)) = (px + q)/(x + 1)(x - 2)}}} 
          {{{highlight((7x - 2)/(x + 1)(x - 2)) = (px + q)/(x + 1)(x - 2)}}} 
                        7x - 2 = px + q --- Equating NUMERATORS, since DENOMINATORS are equivalent
                        7x = px         <font color = red><font size = 3> - 2 = q
                   {{{7x/x = px/x}}}
                  {{{7cross(x)/cross(x) = p*cross(x)/cross(x)}}}____7 = p</font></font></font></font></font></b></pre>