Split the following expression into partial fractions of the form A/(x-3) + B/(4x+2) : (19x-15)/(4x+2)(x-3)

Set the expression equal to the form required in the solution. Multiply both sides by (4x-2)(x-3) to get rid of the denominator and acquire an expression of the form: 19x-15 = A(4x+2) + B(x-3). From here there are a few options to take to solve for A and B. One is to sub in values of x that will result in coefficients of 0 for A and B. Setting x = 3 yields : 42 = 14A i.e. A = 3. Setting x = -0.5 yields: -24.5 = -3.5B i.e. B = 7. solved! An alternate method would involve deriving simultaneous equations from the 19x-15 = A(4x+2) + B(x-3) expression based on the coefficients of x and the constants. i.e equating x terms gives: 4A + B = 19 And equating constants gives: 2A - 3B = -15. These can be solved either by elimination or substitution to again give A=3 B=7