Question

Express the equation (x – 2)/(x – 3) + (x – 4)/(x – 5) = 10/3 ; (x ≠ 3, 5) as a quadratic equation in standard form. Hence, find the roots of the equation so formed.

A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the lawn and the walkway is 360 square metres. The width of the walkway is same on all sides. The dimensions of the lawn itself are 12 metres by 10 metres.