Algebraic Fractions

Question

Hi I am struggling with solving this, I am 12 years old and am trying to work my way through extended maths IGCSE, but have been stumped by this for a few days:

$\dfrac{13x + 2}{(2x + 1)(x - 1)} =\dfrac{A}{2x + 1} + \dfrac{B}{x - 1}$, what are the value of A and B?

I have the answer, A = 3 and B = 5

Answer 1

I believe you use: $$A(x-1)+B(2x+1)=13x+2$$ Then solve $A$ and $B$ using the values of x: $$x-1=0\Rightarrow x=1$$ $$2x+1=0 \Rightarrow x=-\frac12$$

Answer 2

$$A(x-1)+B(2x+1)=x(A+2B)-A+B=13x+2$$ From here we have a system for $A$ and $B$ (two polynomials are equal when corresponding coefficients are equal). Thus, $A+2B=13$ and $-A+B=2$, $A=3$, $B=5$