what is the quotient

Question

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

Answer 1

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].

Answer 2

ru sure

Answer 3

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).

Answer 4

sooo was the answer

Answer 5

The correct answer is:

d) 2(x + 1) / (2x^2 + 5x - 3)