18qrt−2qrs+10rst=018qrt - 2qrs + 10rst = 018qrt−2qrs+10rst=0In the given equation, qqq, rrr, sss, and ttt are positive, and qt\dfrac{q}{t}tq is greater than 5. Which expression is equivalent to sss?A−9qtq−5t\dfrac{-9qt}{q - 5t}q−5t−9qtB9qtq−5t\dfrac{9qt}{q - 5t}q−5t9qtC18qrt18qrt18qrtD2qtq−5t\dfrac{2qt}{q - 5t}q−5t2qtCheck answerShow answerExplanationRearranging: 18qrt+10rst=2qrs18qrt + 10rst = 2qrs18qrt+10rst=2qrs. Factoring: rt(18q+10s)=2qrsrt(18q + 10s) = 2qrsrt(18q+10s)=2qrs. Dividing by rrr: t(18q+10s)=2qst(18q + 10s) = 2qst(18q+10s)=2qs. Expanding: 18qt+10st=2qs18qt + 10st = 2qs18qt+10st=2qs. Rearranging: 18qt=2qs−10st=s(2q−10t)18qt = 2qs - 10st = s(2q - 10t)18qt=2qs−10st=s(2q−10t). Therefore: s=18qt2q−10t=18qt2(q−5t)=9qtq−5ts = \dfrac{18qt}{2q - 10t} = \dfrac{18qt}{2(q - 5t)} = \dfrac{9qt}{q - 5t}s=2q−10t18qt=2(q−5t)18qt=q−5t9qt.
