How do you simplify and state the restrictions for #(p^2-3p-10)/(p^2+p-2)#?

2 Answers
Jun 6, 2018

Answer:

#(-p^2-3p-10)/((p+2)*(p-1))#

Explanation:

Using that #p^2+p-2=(p+2)(p-1)# we get the result above.

Jun 6, 2018

Answer:

#(p-5)/(p-1)#

Explanation:

#"factorise numerator/denominator abd cancel any "#
#"common factors"#

#color(blue)"numerator"#

#"the factors of - 10 which sum to - 3 are - 5 and + 2"#

#p^2-3p-10=(p-5)(p+2)#

#color(blue)"denominator"#

#"the factors of - 2 which sum to + 1 are + 2 and - 1"#

#p^2+p-2=(p+2)(p-1)#

#(p^2-3p-10)/(p^2+p-2)#

#=((p-5)cancel((p+2)))/(cancel((p+2))(p-1))=(p-5)/(p-1)#

#"the denominator cannot equal zero as this would make"#
#"the fraction undefined"#

#p-1!=0rArrp!=1#