Question

How do you simplify `\frac { 7r + 14} { 3r ^ { 2} + r - 10}`?

Answer 1

See a solution process below:

Explanation:

We can factor the numerator and denominator as:

`(7(r + 2))/((r + 2)(3r - 5))`

Now, cancel the common terms:

`(7color(red)(cancel(color(black)((r + 2)))))/(color(red)(cancel(color(black)((r + 2))))(3r - 5)) => 7/(3r - 5)`

Answer 2

`7/(3r-5)`

Explanation:

`"factorise the numerator/denominator"`

`7r+14=7(r+2)larrcolor(blue)"common factor of 7"`

`3r^2+6r-5r-10larrcolor(blue)"factor by grouping"`

`=3r(r+2)-5(r+2)`

`=(r+2)(3r-5)`

`rArr(7r+14)/(3r^2+r-10)`

`=(7cancel((r+2)))/(cancel((r+2))(3r-5))`

`=7/(3r-5)to(r!=5/3)`