Express in simplest form: x2+8x−48x2−144 ÷(4−x) (1 point)
Responses
1x−12
the fraction with numerator 1 and denominator x minus 12
−1x−12
the fraction with numerator negative 1 and denominator x minus 12
−(x+4)(x−4)(x+12)
the fraction with numerator negative open paren x plus 4 close paren and denominator open paren x minus 4 close paren times open paren x plus 12 close paren
(x−4)(x+4)x−12
I'm sorry, but the options you provided don't make sense in the context of expressing the expression in simplest form. However, to simplify the expression, let's start by factoring the numerator and the denominator.
The numerator, x^2 + 8x - 48, can be factored as (x + 12)(x - 4).
The denominator, (4 - x), can be rearranged as (-1)(x - 4).
Now, we can cancel out the common factor of (x - 4), which leaves us with:
(x + 12) / (-1)
Therefore, the expression in simplest form is:
-(x + 12)
To express the given expression in simplest form, we can simplify it step-by-step.
1. First, factor the numerator and denominator:
Numerator: x^2 + 8x - 48 = (x - 4)(x + 12)
Denominator: 4 - x = -(x - 4)
2. Rewrite the expression using the factored form:
(x - 4)(x + 12) / -(x - 4)
3. Cancel out the common factor of (x - 4):
(x + 12) / -1
4. Simplify the expression:
-(x + 12) or -x - 12
Therefore, the simplest form of the expression is -x - 12.
To express the given expression in simplest form, we can simplify it step by step. Here's how we can find the answer:
1. First, let's factor the numerator of the expression, which is x^2 + 8x - 48x^2 - 144. Group the like terms:
x^2 - 48x^2 + 8x - 144
Combine the like terms:
-47x^2 + 8x - 144
2. Next, let's factor the denominator of the expression, which is 4 - x. Rearrange it to simplify the factoring process:
-(x - 4)
3. Now, let's rewrite the expression with the factored numerator and denominator:
(-47x^2 + 8x - 144) / -(x - 4)
4. To simplify the expression further, let's cancel out any common factors between the numerator and the denominator. In this case, there are no common factors to cancel out.
5. Finally, we can write the expression in simplest form:
(-47x^2 + 8x - 144) / -(x - 4)
This is the simplified expression.