"(i) decompose the following expression into partial fractions and
(ii) check your answer by multiplying them out
6x + 7/ 3x (x +1)
Or...you could multiply everything through, group the x terms and the constant terms:
$\displaystyle 6x+7=Ax+A(1)+3Bx$
$\displaystyle 6(x)+7(1)=(A+3B)x+A(1)$
For the two sides to be equal, the coefficients of the two polynomials must be equal. So you "equate the coefficients":
$\displaystyle A+3B=6$ and $\displaystyle A=7$
B is easy to find after that.