Question

A board of length 7 divided by the quantity x minus 2 end of quantity meters was cut into two pieces. If one piece is 3 divided by the quantity x plus 2 end of quantity meters, express the length of the other board, in meters, as a rational expression.

Answer 1

Answer:

Length of other board $=\frac{4x+20}{x^{2} -4}$ metres

Step-by-step explanation:

Given: Length of board = $\frac{7}{x-2}$ metres

Length of board was divided into two.

Length of one piece = $\frac{3}{x+2}$ metres

Let $l$ = length of the other board

Length of the other board = Length of board - Length of one piece

So, $l=\frac{7}{x-2}-\frac{3}{x+2}$

$l=\frac{7(x+2)-3(x-2)}{(x-2)(x+2)} \\\\l=\frac{7x+14-3x+6}{x^{2} -4} \\\\l=\frac{4x+20}{x^{2} -4}$

Thus, length of the other board $=\frac{4x+20}{x^{2} -4}$ metres