Question

Rewrite as equivalent rational expressions with denominator (x – 2)(x – 5)(x – 6)

Answer 1

Rewriting the first term, we have:

`\begin{gathered} (7)/(x^2-7x+10) \\ (7)/((x-5)(x-2))(\text{ Factoring the quadratic expression}) \\ (7\cdot(x-6))/((x-5)(x-2)(x-6))(\text{ Multiplying on both sides by (x-6))} \\ (7x-42)/((x-5)(x-2)(x-6))(\text{ Distributing)} \end{gathered}`

Rewriting the second term, we have:

`\begin{gathered} (4x)/(x^2-8x+12) \\ (4x)/((x-6)(x-2))(\text{ Factoring the quadratic expression}) \\ (4x\cdot(x-5))/((x-6)(x-2)(x-5))(\text{ Multiplying on both sides by (x-5))} \\ (4x^2-20x)/((x-6)(x-2)(x-5))(\text{ Distributing)} \end{gathered}`

The answers are:

`(7x-42)/((x-5)(x-2)(x-6)),(4x^2-20x)/((x-6)(x-2)(x-5))`