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

##### 1 Answer

Mar 18, 2018

#### 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"#