what is the simplified form of x^2-16/4-x
To simplify the expression (x^2 - 16)/(4 - x), first factor out the numerator and denominator:
(x^2 - 16) = (x + 4)(x - 4)
(4 - x) = -(x - 4)
Now, we can rewrite the expression in factored form:
(x + 4)(x - 4)/-(x - 4)
Next, we can cancel out the common factor (x - 4) in the numerator and denominator:
(x + 4)/-1
Finally, simplify the expression:
-(x + 4)
The answers are,
A: - x - 4
B: x + 4
C: x - 4
D: x - 12
To simplify the expression (x^2 - 16)/(4 - x), we can begin by factoring both the numerator and the denominator.
Numerator:
x^2 - 16 can be factored using the difference of squares formula: a^2 - b^2 = (a + b)(a - b)
x^2 - 16 = (x + 4)(x - 4)
Denominator:
4 - x is equivalent to -(x - 4), as mentioned earlier.
Now the expression becomes: (x + 4)(x - 4)/-(x - 4)
We can cancel out the common factor -(x - 4) in the numerator and the denominator, leaving us with (x + 4)/-1.
The negative sign out front (from the denominator) is distributed throughout the expression, resulting in -x - 4.
Therefore, the simplified form of the expression (x^2 - 16)/(4 - x) is A: - x - 4.