Concept:Solve a rational equation by simplifying the numerator and denominator, then cross-multiplying to find y, and finally substitute into 9y+1.Explanation:First, simplify the numerator: 2(3y−4)+6=6y−8+6=6y−2.Simplify the denominator: 3y−(4+5y)=3y−4−5y=−2y−4.The equation becomes −2y−46y−2​=53​.Cross-multiply: 5(6y−2)=3(−2y−4).Expand: 30y−10=−6y−12.Bring terms together: 30y+6y=−12+10, so 36y=−2.Thus y=−362​=−181​.Now compute 9y+1=9×(−181​)+1=−189​+1=−21​+1=21​.Answer:The value of (9y+1) is 21​, which corresponds to option B.