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

AS
Answered by Alec S. Maths tutor

4426 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area beneath the curve with equation f(x) = 3x^2 - 2x + 2 when a = 0 and b = 2


Prove cosec2A-cot2A=tanA


It is given f(x)=(19x-2)/((5-x)(1+6x)) can be expressed A/(5-x)+B/(1+6x) where A and B are integers. i) Find A and B ii) Show the integral of this from 0 to 4 = Kln5


((x^2+4x)/2x)-((x^2-4x)/x)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning