SOlving Complex Fractions
I was not sure exactly how it was set up w/o parethesis so I did it the most complicated way I could think of. Hopefully I'll touch on something that will help.
(X-4)/(X^2-251) + 1/(X-5), then find LCD
(X-4)(X-5)/(X^2-251)(X-5) + (X^2-251)/(X-5)(X^2-251), multiply each side by the other's denomiator to find the LCD, then combine fractions
((X-4)(X-5) + (X^2-251)) / (X^2-251)(X-5) , then factor out
X^2 -9X + 20 + X^2 - 251 / (X^2-251)(X-5) , combine terms and get ready for partial fractions
(2X^2 -9X -231) / (X^2-251)(X-5), partial fractions
(2X^2 -9X -231) / (X^2-251)(X-5) = A/(X-5) + (B+CX)/(X^2-251), now solve for A, B, and C.
(2X^2 -9X -231)= A(X^2-251) + (BX+C)(X-5), expand out
AX^2-A251+BX^2-B5+CX-C251, it gets tricky here, I always put the x terms together like so...
Now remove the X variables and solve... C=-9,A=(2028/251),B=(1429/753)
Judging by the answers I either did it wrong or you don't need to do a paritial fraction. Let me know if you needed to solve it a different way.