Final answer:
To rationalize the denominator and simplify the expression 337/217, multiply the numerator and denominator by the conjugate of the denominator. Then, divide the resulting expression by their greatest common factor.
Step-by-step explanation:
To rationalize the denominator and simplify the expression 337/217, we need to multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 217 is -217, so we multiply both the numerator and denominator by -217, as shown:
(337 * -217) / (217 * -217) = -72929 / 47169
Then, we simplify the expression by dividing the numerator and denominator by their greatest common factor:
-72929 / 47169 = -2063 / 1331