Question

Simplify surd need an answer asap please

Answer 1

Explanation:

Simplify Surd:

• Multiply the denominator and numerator with the conjugate of the denominator.

• Conjugate of denominator:

`\sf (√(x+1)) + (√(x-1))`

`\sf(√(x+1) +√(x-1))/(√(x+1)-√(x-1)) = ((√(x+1) +√(x-1))(√(x+1) +√(x-1)))/((√(x+1) -√(x-1))(√(x+1) +√(x-1)))\\`

When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²

`\sf =((√(x+1) +√(x-1))^2)/((√(x+1))^2 - (√(x-1))^2)\\\\=((√(x+1))^2+(√(x-1))^2+2*√(x+1)*√(x-1))/(x + 1 - (x - 1))\\\\=(x+1 +x -1 + 2*√((x+1)(x-1)))/(x + 1 - x + 1)\\\\=(x+ x + 1 - 1 +2√(x^2-y^2))/(x-x+1+1)\\\\=(2x+2√(x^2-y^2))/(2)\\\\= (2x)/(2)+(2√(x^2-y^2))/(2)\\\\=x + √(x^2-y^2)`