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

1 Answer

7 votes

Answer:


= (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

User Audrey Dutcher
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