Row Reduction & Rank · Medium problem

A partial-fraction decomposition requires $\dfrac{5x+7}{(x+1)(x+2)} = \dfrac{A}{x+1}+\dfrac{B}{x+2}$ for all $x$. Clearing denominators gives $5x+7=A(x+2)+B(x+1)$. Matching the coefficient of $x$ and the constant term gives a linear system in $A,B$. Find $B$.