simplify
(numbers AFTER the variable represent exponents)
ALSO these are all fractions, theres just no way to put the line
x2-64 . x2-x-6 _ 1
x2-4x-12 x2+5x-24 x-6
use x^3 to say x cubed
use brackets to enclose the denominators
and / to show division, * to show multiplication
e.g.
(x^2-64)/(x+2)
To simplify the given expression, follow these steps:
Step 1: Factorize the expressions in the numerator and denominator.
- We will factorize the numerator: x^2 - 64. This is a difference of squares, so it can be factored as follows: (x - 8)(x + 8).
- Next, factorize the first part of the denominator, x^2 - 4x - 12. This can be factored as follows: (x - 6)(x + 2).
- Similarly, factorize the second part of the denominator, x^2 + 5x - 24. This factors as (x - 3)(x + 8).
The expression becomes: ((x - 8)(x + 8)) / ((x - 6)(x + 2)(x - 3)).
Step 2: Cancel common factors.
- In the numerator, we can cancel out the (x + 8) term with one of the (x + 8) terms in the denominator.
- Similarly, we can cancel out the (x - 6) term in the numerator with one of the (x - 6) terms in the denominator.
The expression simplifies to: (x - 8) / ((x + 2)(x - 3)).
So, the simplified form of the given expression is: (x - 8) / ((x + 2)(x - 3)).