Question

Divide the rational expectations express in simplest form. Numerator and denominator must be in variable form.

Answer 1

Given the expression in the image, we first get the resulting fraction from the calculations though the following steps.

Step 1: We factorise the 4 quadratic equations:

$9x^2+3x-20$

Factors of the equation above after factorisation will be;

$\begin{gathered} 9x^2+3x-20 \\ (3x-4)(3x+5) \end{gathered}$

Equation 2:

$3x^2-7x+4_{}$

Factors of the equation above after factorisation will be;

$\begin{gathered} 3x^2-7x+4 \\ (x-1)(3x-4) \end{gathered}$

Equation 3:

$6x^2+4x-10$

Factors of the equation above after factorisation will be;

$\begin{gathered} 6x^2+4x-10 \\ 2(x-1)(3x+5) \end{gathered}$

Equation 4:

$x^2-2x+1$

Factors of the equation above after factorisation will be;

$\begin{gathered} x^2-2x+1 \\ (x-1)(x-1) \end{gathered}$

Step 2: To compute the division, we have

$\begin{gathered} \frac{(3x-4)(3x+5)}{(x-1)(3x-4)}\text{ divided by} \\ \\ \frac{2(x-1)(3x+5)}{(x-1)(x-1)} \end{gathered}$

We have:

$\begin{gathered} \frac{(3x+5)}{(x-1)}\text{ divided by} \\ \\ \frac{2(3x+5)}{(x-1)} \end{gathered}$

This gives us:

$\begin{gathered} \frac{3x+5}{x-1}\times\frac{x-1}{2(3x+5)} \\ \text{After division, we have:} \\ \frac{1}{2} \end{gathered}$

From the final fraction which is 1/2, it can be seen that the numerator is 1 while the denominator is 2.