Question

How do you divide `\frac{x^2-25}{x+3} \-: (x-5)`?

Answer 1

We can use the rule about division of rational expressions where you can change the division in a multiplication by flipping the second fraction (where, in your case, the second "fraction" can be written as `(x-5)/1`).

In our case you have:

`(x^2-25)/(x+3)-:(x-5)/1=(x^2-25)/(x+3)xx1/(x-5)`

We can now manipulate the numerator of the first fraction as:

`x^2-25=(x+5)*(x-5)`

Substituting and simplifying:

`((x+5)*(x-5))/(x+3)xx1/(x-5)=(x+5)/(x+3)`