Final answer:
The total length of all edges of a cube when one edge is given by (2x-8)/(72x+24) can be found by simplifying the edge's expression, then multiplying by 12, as a cube has 12 edges. For a numerical answer, the value of x needs to be known.
Step-by-step explanation:
The question involves finding the total length of all edges of a cube when one edge of the cube is given by the expression (2x-8)/(72x+24). A cube has 12 edges in total, and each edge is of the same length. To find the total length of all the edges, we need to simplify the given expression for one edge and then multiply by 12.
Firstly, we can simplify the edge expression by factoring out common factors in the numerator and the denominator. The denominator 72x + 24 can be factored as 24(3x + 1). There is no common factor in the numerator and the denominator, so the expression for the edge remains (2x-8)/(72x+24). To obtain the total length of the edges of the cube, we multiply the edge length by 12, which leads to 12((2x-8)/(72x+24)).
To find an exact numerical answer, x would need to be specified, as the expression depends on the value of x.