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} ((3x-4)(3x+5))/((x-1)(3x-4))\text{ divided by} \\ \\ (2(x-1)(3x+5))/((x-1)(x-1)) \end{gathered}`

We have:

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

This gives us:

`\begin{gathered} (3x+5)/(x-1)*(x-1)/(2(3x+5)) \\ \text{After division, we have:} \\ (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.