How do you simplify #\frac { r ^ { 2} - 14r + 33} { r - 11}#?

2 Answers

# r-3#

Explanation:

#r^2-14r+33=r^2-11r-3r+33#

#=r (r-11)-3 (r-11)#

#=(r-3)(r-11)#

Thus
#r^2-14r+33=(r-3)(r-11)#

Dividing by #r-11#, we get
Answer is #r-3#

Jan 30, 2018

#r-3#

Explanation:

In the fraction #" "(r^2 -14r +33)/(r-11)" "#

you MAY NOT cancel anything, however tempting it looks.

There are plus and minus signs which means there are 3 terms in the numerator and 2 terms in the denominator.

Only factors can be cancelled.

Factorise where possible.

Find factors of 33 which add to 14. #" "(11 and 3# will do nicely!)

#(r^2 -14r +33)/(r-11) = ((r-11)(r-3))/((r-11))#

Now that you have factors, you may cancel.

#(cancel((r-11))(r-3))/cancel((r-11))#

#=r-3#