Question 1113597
<br>
{{{A/(x-1)+B/(x+4) = 2x/(x^2+3x-4) = 2x/((x-1)(x+4))}}}<br>
Multiply both sides by the LCM, (x-1)(x+4):<br>
{{{A(x+4)+B(x-1) = 2x)}}}
{{{(A+B)x + (4A-B) = 2x}}}<br>
Equate the coefficients of the terms on the two sides of the equation:<br>
{{{A+B=2}}}; {{{4A-B=0}}}<br>
Solve the pair of equations.<br>
(you can do the work...)<br>
Answer: A=2/5; B=8/5