Home > Algebra > Division of Rational Expressions

How do you simplify #(x^2-8x+16 )/(x^2-12x+32 )#?

Answer 1

Eli Assouline

#(x-4)/(x-8)#

Consider#" "x^2-8x+16#

Notice that #4xx4=16" and "4+4=8#

#(x-4)(x-4)=(x-4)^2# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider #" "x^2-12x+32#

notice that #4xx8=32" and "8+4=12#

#(x-4)(x-8)# '~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Putting it all together")#

#(x^2-8x+16)/(x^2-12x+32) = ((x-4)(x-4))/((x-4)(x-8))#

#=>(x-4)/(x-4)xx(x-4)/(x-8)#

But #(x-4)/(x-4) =1# giving:

#(x-4)/(x-8)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Avery Alexander

To simplify the expression (x^2-8x+16)/(x^2-12x+32), we can factor both the numerator and denominator.

The numerator can be factored as (x-4)(x-4), and the denominator can be factored as (x-4)(x-8).

By canceling out the common factor of (x-4), we are left with (x-4)/(x-8) as the simplified form of the expression.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.