Write in simplest form?

Question

[(x^2-4x-60)/(x^2-100)]

Answer 1

(x² - 4x - 60)/(x² - 100)

Numerator = x² - 4x -60
= (x - 10)(x + 6)

Denominator = x² - 100
= x² - 10²
= (x - 10)(x + 10)

So (x² - 4x - 60)/(x² - 100)
= (x - 10)(x + 6)/[(x - 10)(x + 10)]

= (x + 6)/(x + 10)

Answer 2

(x^2-4x-60)/(x^2-100)

If the numerator and denominator can be factored and they have a factor in common, the common factor can be cancelled out.

x^2 - 100 = (x + 10)(x - 10) [difference of two squares]

Looking at the numerator, you hope that one of its factors is (x - 10) [because the coefficient of the x term is -4]

x^2 - 4x - 60 = (x - 10)(x + 6)

The fraction is now

(x - 10)(x + 6)/(x + 10)(x - 10)

(x + 6)/(x + 10)

Answer 3

Denominator is easiest: it's the difference of two squares and thus is factored to the sum and difrference:

x^2-100 = (x-10)*(x+10)

For the numerator, can you find two numbers that
when multiplied = -60
and
when added equal -4 ?

How about -10 and +6 ?

So, the numerator is factored into (x-10)*(x+6) right?

Put it together and cancel the common factor on top and bottom

Answer 4

x^2-4x-60 = (x-10)(x+6)

x^-100 = (x-10)(x+10) give the a^2 - b^2 = (a-b) (a+b)

so we get

(x-10)(x+6)
------------------------
(x-10) (x+10)

Answer: (x+6)/(x+10)

Answer 5

x+6
-----
x+10

Answer 6

[(x^2-4x-60)/(x^2-100)]
(x-10)(x+4)/((x-10)(x+10))

(x+4)/(x+10)

Answer 7

(x^2-4x-60)/(x^2-100)=((x-2)^2-64)/(x^^2-10^2)
=((x-2)^2-8^2)/(x^2-10^2)
=(x-2-8)(x-2+8)/(x-10)(x+10)
=(x-10)(x+6)/(x-10)(x+10)
=(x-6)/(x+10)=(x+10-16)/(x+10)=1-16/(x+10)