How do you solve sqrt(1-(9/x^2))? I know the answer is sqrt x^2 -9/x but I'm not sure how to get the answer on my own. If you could show steps on how to get the answer that would help me a lot!
To solve the expression sqrt(1-(9/x^2)), you can follow these steps:
Step 1: Start by simplifying the expression inside the square root.
sqrt(1 - (9/x^2)) = sqrt((x^2 - 9)/x^2)
Step 2: Notice that (x^2 - 9) can be factored as a difference of squares.
sqrt((x^2 - 9)/x^2) = sqrt(((x - 3)(x + 3))/x^2)
Step 3: Split the square root into separate square roots for both the numerator and denominator.
sqrt(((x - 3)(x + 3))/x^2) = (sqrt((x - 3)(x + 3))) / (sqrt(x^2))
Step 4: Simplify each square root separately.
sqrt(x - 3) * sqrt(x + 3) / sqrt(x^2)
Step 5: Cancel out common terms. The square root of x^2 simplifies to x.
(sqrt(x - 3) * sqrt(x + 3)) / x
So, the final simplified expression is sqrt x^2 - 9/x.