what is the quotient
x^2-16/2x^2-9+4 / 2x^2+14x+24/4x+4
a) 1/x+3
b) 2x+2/x+3
c) 2x+2/2x^2+5x-3
d) 2(x+1)/2x^2-5x-3
To find the quotient, we first need to simplify both the numerator and the denominator separately and then divide.
Given:
Numerator = x^2 - 16
Denominator = 2x^2 - 9 + 4
Simplify the numerator:
x^2 - 16 is a difference of squares, so it can be factored as (x + 4)(x - 4).
The numerator simplifies to (x + 4)(x - 4).
Simplify the denominator:
2x^2 - 9 + 4
Combine the constants:
2x^2 - 5
This does not factor any further.
Next, let's divide the two fractions:
(x^2 - 16)/(2x^2 - 5) divided by (2x^2 + 14x + 24)/(4x + 4)
This is equivalent to:
[(x + 4)(x - 4)] / [2x^2 - 5] divided by [2(x^2+7x+12)] / 4(x + 1)
Simplify further by multiplying by the reciprocal:
[(x + 4)(x - 4)(4)(x+1)] / [2(x^2 - 5)(x^2+7x+12)]
Now we simplify:
[(x + 4)(x - 4)(4)(x+1)] / [2(x - 1)(x - 4)((x+5)(x+3))]
Therefore, the correct answer is d) 2(x + 1)/[2x^2 - 5x - 3].
ru sure
I apologize for the mistake in my previous response. Let's go through the calculation again.
Given:
Numerator = x^2 - 16
Denominator = 2x^2 - 9 + 4
Numerator simplifies to (x + 4)(x - 4).
Denominator simplifies to 2x^2 - 5.
Now we have:
[(x + 4)(x - 4)] / [2x^2 - 5] divided by [2x^2 + 14x + 24] / [4x + 4]
This is equivalent to:
[(x + 4)(x - 4)] / [2x^2 - 5] / [2(x^2 + 7x + 12)] / [4(x + 1)]
Now simplify by multiplying with the reciprocal:
[(x + 4)(x - 4)] / [2x^2 - 5] * [4(x + 1)] / [2(x + 3)(x + 4)]
After simplifying further, we get:
2(x + 1) / (2x^2 + 5x - 3)
So, the correct answer is d) 2(x + 1) / (2x^2 + 5x - 3).
sooo was the answer
The correct answer is:
d) 2(x + 1) / (2x^2 + 5x - 3)