Walking the stairs

Algebra Level pending

Betty the monkey draws a staircase on a 3 by 4 foot rectangle, then she shades the area of the of the part of the paper not drawn on by the staircase red, the steps under the staircase and the staircase blue. We know that 1. the staircase goes either from the top-left corner to the bottom-left corner, or the bottom-left corner to the top-right corner. 2. That the steps are the same size. 3. They go in a perfect diagonal. Write the function(s) that gives the area of the red section/ over the area of the blue section where x is the number of steps in the stair case. Select all that apply

((x-1)+(x-2)+(x-3)...+(x-x))/((x)+(x-1)+(x-2)...+(x-x) ((x)+(x-1)+(x-2)...+(x-x)/12 ((x)+(x-1)+(x-2)...+(x-x)/((x-1)+(x+2)+(x-3)...(x-x) ((x-1)+(x-2)+(x-3...+(x-x)/12

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