Question

Rationalise the denominator and simplify (7+3√5/3+√5) - (7-3√5/3-√5)​

Answer 1

Answer:

√5

Step-by-step explanation:

(7+3√5)/(3+√5)-(7-3√5)/(3-√5)

=(7+3√5)/(3+√5)×(3-√5)/(3-√5)-(7-3√5)/(3-√5)×(3+√5)/(3+√5)

=(7+3√5)×(3-√5)/(3×3)-(√5×√5)-(7-3√5)(3+√5)/(3×3)-(√5×√5)

=(21-7√5+9√5-15)/(9-5)-(21+7√5-9√5-15)/(9-5)

=(21-7√5+9√5-15-21-7√5+9√5+15)/4

=(-14√5+18√5)/4

=(4√5)/4

=√5