Find integers A and B, such that (5x +4)/((2-x)(1+3x)) = A/(2-x) + B/(1+3x)
Adding the fractions on the RHS of the equation in the usual way gives
A/(2-x) + B/(1+3x) = (A(1+3X) +B(2-X))/((2-X)(1+3X)) = (5x +4)/((2-x)(1+3x))
This gives an expression for the original numerator in terms of A B and x.
A(1+3X) +B(2-X)) = 5x +4
Take values of x which simplify the equation e.g x = 2, -1/3
Gives A = 2, B = 1
So (5x +4)/((2-x)(1+3x)) = 2/(2-x) + 1/(1+3x)
LF
Related Maths A Level answers
All answers ▸When dealing with trigonometric functions such as sin, cos or tan, how do you solve the trigonometric equation when the argument of the function(s) is nx, where n is a real number not equal to 1.
Find the first 3 terms and the sum to infinity of a geometric series with first term, 10 and common ratio 0.2
Differentiate with respect to x, y = (x^3)*ln(2x)
Integrate the following function: f(x) = ln(x)