Question

Find the perimeter of quadrilateral. Express it in simplest form.

Short answer

Hence the perimeter of given quadrilateral is$\frac{13x^2+4x-9}{2x\left(x^2-1\right)}$

Step-by-step solution

Step 1. Write down the given information.

The given quadrilateral is shown below.

Step 2. Evaluating the perimeter of given quadrilateral.

The perimeter $\left(P\right)$ of the given quadrilateral is equal to the sum of length of its sides. Therefore, perimeter of given quadrilateral is evaluated as:

$\begin{array}{c}P=\frac{4}{x^2-1}+\frac{3}{2x}+\frac{2}{x+1}+\frac{3}{x}\\ =\frac{4}{\left(x-1\right)\left(x+1\right)}+\frac{3}{2x}+\frac{2}{x+1}+\frac{3}{x}\\ =\frac{8x+3\left(x-1\right)\left(x+1\right)+4x\left(x-1\right)+6\left(x-1\right)\left(x+1\right)}{2x\left(x-1\right)\left(x+1\right)}\\ =\frac{8x+3\left(x^2-1\right)+4x^2-4x+6\left(x^2-1\right)}{2x\left(x^2-1\right)}\\ =\frac{8x+3x^2-3+4x^2-4x+6x^2-6}{2x\left(x^2-1\right)}\\ =\frac{13x^2+4x-9}{2x\left(x^2-1\right)}\end{array}$

Step 3. Conclusion.

Hence the perimeter of given quadrilateral is$\frac{13x^2+4x-9}{2x\left(x^2-1\right)}$