Question

Simplify the rational expression defining the function. f(x)=(2x-2)/(x²+2x-3) simplifies to f(x)= where x!=1.

Answer 1

To simplify the rational expression (2x-2)/(x²+2x-3) where x!=1, factor the denominator and cancel out common factors to get f(x)=2/(x+3).

Step-by-step explanation:

To simplify the rational expression defining the function f(x) = (2x-2)/(x²+2x-3) where x != 1, we can factor the denominator:

x² + 2x - 3 = (x + 3)(x - 1)

Then, we can cancel out the common factors between the numerator and denominator:

f(x) = (2(x - 1))/((x + 3)(x - 1))

Finally, we are left with:

f(x) = 2/(x + 3)