Concept:Use the partial fraction method and choose a suitable value of x to eliminate one term, making it easy to find R.Explanation:Start with the given equation:(x+4)(x−3)15−2x=x+4R+7(x−3)9Multiply both sides by the common denominator 7(x+4)(x−3):7(15−2x)=7R(x−3)+9(x+4)Put x=−4 so that 9(x+4) becomes zero and only the term with R remains.At x=−4:7(15−2(−4))=7R(−4−3)+07(15+8)=7R(−7)7×23=−49R161=−49RR=−49161=−723Answer:R=−723This corresponds to option B.