Rationalise the expression 1/(�ã2 + �ã3).
Multiply 1/(√2 + �√3)
by (√2 - �√3)/(√2 - �√3)
to get (√2 - �√3)/-1
or
(√3 - √2)
To rationalize the expression 1/(√2 + √3), we can multiply the numerator and the denominator by the conjugate of the denominator, which is (√2 - √3). This will eliminate the square roots in the denominator.
To do this, we multiply the numerator and denominator by (√2 - √3):
1/(√2 + √3) * (√2 - √3)/(√2 - √3)
Multiplying these expressions together gives:
(√2 - √3)/( (√2 + √3) * (√2 - √3))
Next, we simplify the denominator using the formula (a + b)(a - b) = a² - b². Applying this formula to (√2 + √3) * (√2 - √3), we get:
(√2)² - (√3)²
Simplifying this further gives:
2 - 3
Now, we have:
(√2 - √3)/(2 - 3)
= (√2 - √3)/(-1)
Finally, we can distribute the negative sign to the terms inside the numerator:
= - (√2 - √3)/1
= - (√2 - √3)
So, the rationalized expression for 1/(√2 + √3) is - (√2 - √3).