im not sure how to solve this:
x^2
--- -9
x^2-9
retype in a line expression using brackets.
To solve the expression (x^2 / (x^2-9)) - 9, you can follow these steps:
Step 1: Factor the denominator:
The denominator, x^2 - 9, can be factored using the difference of squares formula: a^2 - b^2 = (a + b)(a - b). Applying this formula, we get (x + 3)(x - 3).
Step 2: Rewrite the expression:
Now, rewrite the expression using the factored denominator: (x^2 / ((x + 3)(x - 3))) - 9.
Step 3: Find a common denominator:
To simplify the expression, you need to find a common denominator. The common denominator will be (x + 3)(x - 3).
Step 4: Determine the numerator:
The numerator of the first fraction, x^2, already has the correct denominator.
Step 5: Adjust the second fraction:
The second fraction, 9, can be rewritten with the common denominator (x + 3)(x - 3) as 9 * ((x + 3)(x - 3) / ((x + 3)(x - 3))). Simplify this expression to 9(x + 3)(x - 3).
Step 6: Combine the fractions:
Substitute the adjusted second fraction into the expression: (x^2 / ((x + 3)(x - 3))) - 9(x + 3)(x - 3) / ((x + 3)(x - 3)).
Step 7: Simplify the expression:
To simplify further, multiply out the denominators: (x^2 - 9(x + 3)(x - 3))/(x + 3)(x - 3).
Step 8: Simplify the numerator:
Now, simplify the numerator by expanding: (x^2 - 9(x^2 - 9))/(x + 3)(x - 3). This gives (x^2 - 9x^2 + 81)/(x + 3)(x - 3).
Step 9: Combine like terms:
Combine like terms in the numerator: (-8x^2 + 81)/(x + 3)(x - 3).
So, the simplified expression is (-8x^2 + 81)/(x + 3)(x - 3).