Final answer:
To rationalize the denominator of 1/(√2+1)(√3-1), we multiply the fraction by the conjugate, which is (√2-1)(√3+1)/(√2-1)(√3+1), and then simplify to obtain a rational denominator.
Step-by-step explanation:
To rationalize the denominator of the expression 1/(√2+1)(√3-1), we need to get rid of the radicals in the denominator. The process usually involves multiplying the numerator and the denominator by the conjugate of the denominator. The conjugate of (√2+1)(√3-1) is (√2-1)(√3+1). So we multiply the fraction by (√2-1)(√3+1)/(√2-1)(√3+1).
The result will be:
[(√2-1)(√3+1)] / [(√2+1)(√3-1)(√2-1)(√3+1)]
Expanding the denominator will give us a difference of squares, which removes the radical and simplifies the expression. We will have:
(√2√3 + √2 - √3 - 1) / [(2-1)(3-1)]
Simplified further, the expression becomes:
(√6 + √2 - √3 - 1) / 2
Now the denominator is rationalized, and this concludes the process.