Question

Show that 1/ 1+ √2 + 1 /√2+√3 = -1 + √3

Answer 1

See below.

Explanation:

1/( 1+√2) + 1 /(√2+√3)

Multiply both fractions by the conjugate of the denominators:

= (1 -√2) / (1 +√2)(1 - √2) + (√2 - √3) / (√2 + √3)(√2 - √3)

= (1 - √2) / -1 + (√2 - √3) / -1

= -1 + √2 - √2 + √3

= -1 + √3 as required.