Question

(1/(\sqrt{a}-3)+1/(\sqrt{a} +3))*(1-3/(\sqrt{a} ))

Answer 1

`(2(√(a) - 3))/(a - 9)`

Explanation:

`((1)/(√(a)-3)+(1)/(√(a) +3)) * (1 - (3)/(√(a))) =`

`= (1)/(√(a)-3) +(1)/(√(a) +3)} - (3)/(√(a)(√(a)-3)) - (3)/(√(a)(√(a) +3))`

`= (√(a)(√(a)+3))/((√(a)-3)√(a)(√(a)+3))+(√(a)(√(a)-3))/((√(a) +3)√(a)(√(a)-3))`

`~~~~~- (3(√(a)+3))/(√(a)(√(a)-3)(√(a)+3))-(3(√(a)-3))/(√(a)(√(a) +3)(√(a)-3))`

`= (a + 3√(a) + a - 3√(a) - 3√(a) - 9 - 3√(a) + 9)/(√(a)(√(a) +3)(√(a)-3))`

`= (2a - 6√(a))/(√(a)(√(a) +3)(√(a)-3))`

`= (2(a - 3√(a))/((a - 9)√(a))`

`= (2(√(a)√(a) - 3√(a))/((a - 9)√(a))`

`= (2√(a)(√(a) - 3))/((a - 9)√(a))`

`= (2(√(a) - 3))/(a - 9)`