Simplify. The quantity x squared plus 3 times x minus 4 over the quantity x plus 4
A. 1 over the quantity x minus 4, where x does not equal 4
B. x minus 4
C. x minus 1, where x does not equal 1
D. x minus 1, where x does not equal negative 4
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To simplify the expression, we can use polynomial division or factorization. Factoring the numerator, we get:
x^2 + 3x - 4 = (x + 4)(x - 1)
Then, we can rewrite the expression as:
(x + 4)(x - 1) / (x + 4)
The (x + 4) terms cancel out, leaving us with:
x - 1
Therefore, the answer is C. x - 1, where x does not equal 1.
please answer the question with one of the multiple choice questions
The answer is C. x - 1, where x does not equal 1.
To simplify the expression, x^2 + 3x - 4 / (x + 4), we need to factor the numerator and see if any common factors can be canceled out.
The numerator can be factored as (x - 1)(x + 4).
Now we can rewrite the expression as (x - 1)(x + 4) / (x + 4).
We observe that (x + 4) appears in both the numerator and denominator. Therefore, we can cancel out (x + 4).
The simplified expression is x - 1.
So, the correct answer is D. x - 1, where x does not equal negative 4.
To simplify the expression (x^2 + 3x - 4) / (x + 4), you can use the factoring method.
Step 1: Factor the numerator (x^2 + 3x - 4).
The factors of the quadratic expression can be determined by finding two numbers that multiply to -4 and add up to 3. The factors are (x + 4) and (x - 1). Therefore, the numerator can be factored as (x + 4)(x - 1).
Step 2: Simplify the expression.
Now, you can cancel out the common factor of (x + 4) in the numerator and denominator. After canceling, the expression simplifies to (x - 1) / 1.
The simplified expression is (x - 1), which corresponds to option C: x minus 1, where x does not equal 1.