Question 1162547
<br>
{{{(8x^2+10x+20)/(x(x+4)(x+5)) = A/x+B/(x+4)+C/(x+5)}}}<br>
Multiply by the least common denominator....<br>
{{{A(x+4)(x+5)+B(x)(x+5)+C(x)(x+4) = 8x^2+10x+20}}}
{{{A(x^2+9x+20)+B(x^2+5x)+C(x^2+4x) = 8x^2+10x+20}}}<br>
Equate coefficients:<br>
(1) {{{A+B+C = 8}}}
(2) {{{9A+5B+4C = 10}}}
(3) {{{20A = 20}}}<br>
Equation (3) immediately gives us A=1.  Substituting in (1) and (2) gives us<br>
(4) {{{B+C = 7}}}
(5) {{{5B+4C = 1}}}<br>
Solve by elimination....<br>
{{{4B+4C = 28}}}
{{{4B+5C = 1}}}
{{{C = -27}}}<br>
Then<br>
{{{B = 34}}}<br>
ANSWER:<br>
{{{(8x^2+10x+20)/(x(x+4)(x+5)) = 1/x+34/(x+4)-27/(x+5)}}}<br>