Mathematics √2 ÷ √10 - √2.

To simplify this expression, we first need to rationalize the denominator by multiplying both the numerator and denominator by √10:

(√2 / √10 - √2) * (√10 / √10)
= (√2 * √10 / 10 - √2 * √10) / 10
= (√20 / 10 - √20) / 10
= (√20 - 10√20) / 10
= -9√20 / 10
= -9√2 / 10
= -9√2 / 10

Therefore, √2 ÷ √10 - √2 simplifies to -9√2 / 10.

√2 ÷ √10 - √2

= √2/√10 - √2

= √2(1/√10 - 1)

= √2(√10/10 - 1)

= √2(√10 - 10)/10

= (√2√10 - 10√2)/10

= (2√5 - 10√2)/10

= 2√5/10 - 10√2/10

= 2√5/10 - 5√2/5

= (2√5 - 5√2)/5

Therefore, the answer is (2√5 - 5√2)/5.