Question

How do you simplify `(x+5)/(3x^2+14x-5)` and what are the excluded values of the variables?

Answer 1

`1/(3x-1)" excluded value "x!=1/3`

Explanation:

`"factorise the denominator using the a-c method"`

`"the factors of - 15 which sum to + 14 are + 15 and - 1"`

`3x^2+15x-x-5larrcolor(blue)"split the middle term"`

`=color(red)(3x)(x+5)color(red)(-1)(x+5)larrcolor(blue)"factor by grouping"`

`"take out "color(blue)"common factor "(x+5)`

`=(x+5)(color(red)(3x-1))`

`rArr(cancel((x+5)))/(cancel((x+5))(3x-1))`

`=1/(3x-1)`

`"the excluded values are any values of x which make "`
`"the denominator zero"`

`3x-1=0rArrx=1/3larrcolor(red)"excluded value"`