Question

How do you write the mixed expression `(d-6)+(d+1)/(d-7)` as a rational expression?

Answer 1

`(d^2-12d+43)/(d-7)`

Explanation:

We require to multiply `(d-6)" by " (d-7)/(d-7)`

`rArr((d-6)(d-7))/(d-7)+(d+1)/(d-7)`

The fractions now have a `color(blue)"common denominator"` so we can add the numerators while leaving the denominator as it is.

`rArr(d^2-13d+42+d+1)/(d-7)`

`=(d^2-12d+43)/(d-7)larrcolor(red)" rational expression"`