f(x)=x^2 -1 and g(x)=x-1, which expression represents f(x)/g(x) for x>1?

Question

Learning about function expression.

 

 

How to determine which expression represents f(x) and g(x)

Answer 1

Hi Lisa;

f(x)/g(x)

(x²-1)/(x-1)

x cannot equal 1 because this would render the denominator, also known as the divisor, as zero.

x can be greater than 1.

If you would like, we can factor the numerator...

x²-1

(x+1)(x-1)

FIRST...(x)(x)=x²

OUTER...(x)(-1)=-1x=-x

INNER...(1)(x)=1x=x

LAST...(1)(-1)=-1

x²-x+x-1

x²-1

So...

f(x)/g(x)=[(x+1)(x-1)]/(x-1)

(x-1) is in the numerator and denominator.  It cancels...

f(x)/g(x)=(x+1)