After Rationalizing the numerator and simplifying, Sqrt x^2+100 (end sqrt) -10 /x^2

Question

Hello I need very much help with this question, the x^2+100 is under the square root and the -10 is not included in the square root. Then that is over x^2.

Answer 1

Multiply the numerator and denominator by the conjugate of the numerator √(x²+100) + 10 to get:

[(√(x²+100) - 10)(√(x²+100) + 10) / [x²(√(x²+100) + 10)] = [x²+100 - 100] / [x²(√(x²+100) + 10)] =

1 / (√(x²+100) + 10)

Answer 2

Try multiplying the numerator and denominator by sqrt(x² + 100) + 10, and see what you can simplify after that.