Question

\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}

Answer 1

`= (2x-3√(x) )/(x-1)`

Explanation:

Given the expression

`((√(x) +1)^(2) +(√(x) -1)^(2) ))/((√(x) +1)(√(x) -1)) -(3√(x) +1)/(x-1)`

Expand

`((√(x) +1)^(2) +(√(x) -1)^(2) ))/((√(x) +1)(√(x) -1)) -(3√(x) +1)/(x-1)\\= (x+2√(x)+1+(x-2√(x) +1) )/(x-1)- (3√(x) +1)/(x-1)\\= (2x+1)/(x-1) - (3√(x) +1)/(x-1)\\= (2x+1-(3√(x) +1))/(x-1)\\= (2x-3√(x) +1-1)/(x-1)\\= (2x-3√(x) )/(x-1)`

This gives the simplified form