Rationalize the denominator.
2 / squareroot7+squareroot 3
Show steps
To rationalize the denominator of the given expression (2 / √7 + √3), we need to get rid of the square roots in the denominator. This can be achieved by multiplying the numerator and the denominator by the conjugate of the denominator, which is the same expression but with the opposite sign between the two square roots.
Step 1: Identify the denominator and its conjugate.
Denominator: √7 + √3
Conjugate: √7 - √3
Step 2: Multiply the numerator and the denominator by the conjugate.
(2 / √7 + √3) * (√7 - √3 / √7 - √3)
Step 3: Simplify the expression.
Using the distributive property, expand the expression:
(2√7 - 2√3) / ((√7)^2 - (√3)^2)
Simplify further:
(2√7 - 2√3) / (7 - 3)
Final step: Simplify the expression.
(2√7 - 2√3) / 4
The rationalized form of the expression 2 / √7 + √3 is (2√7 - 2√3) / 4.