Question

what is the quotient of (x^(2)-16)/(2x^(2)-9x+4)-:(2x^(2)+14x+24)/(4x+4)

Answer 1

The answers are,
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 2

To divide these two fractions, we first need to rewrite the division operation as multiplication by taking the reciprocal of the second fraction.

So, the given expression: (x^2 - 16)/(2x^2 - 9x + 4) ÷ (2x^2 + 14x + 24)/(4x + 4)

Simplify this to: (x^2 - 16)/(2x^2 - 9x + 4) * (4x + 4)/(2x^2 + 14x + 24)

Now, simplify the fractions separately:
1. (x^2 - 16)/(2x^2 - 9x + 4)
Factor the numerator and denominator: (x + 4)(x - 4)/(2x - 1)(x - 4)
This simplifies to: (x + 4)/(2x - 1)

2. (4x + 4)/(2x^2 + 14x + 24)
Factor the numerator: 4(x + 1)
Factor the denominator: 2(x + 4)(x + 3)
This simplifies to: 2/(x + 3)

Now, multiply the simplified fractions:
(x + 4)/(2x - 1) * 2/(x + 3)
= 2(x + 4)/(2x - 1)(x + 3)
= 2(x + 4)/(2x^2 + 6x - x - 3)
= 2(x + 4)/2(x^2 + 5x - 3)
= (x + 4)/(x^2 + 5x - 3)

Therefore, the quotient of the given expression is: (x + 4)/(x^2 + 5x - 3)

Answer 3

To find the quotient of the given expression, we'll simplify both fractions and then divide them.

Given expression: (x^2 - 16)/(2x^2 - 9x + 4) ÷ (2x^2 + 14x + 24)/(4x + 4)

Simplify the two fractions:
1. (x^2 - 16)/(2x^2 - 9x + 4)
Factor numerator and denominator: (x + 4)(x - 4)/(2x - 1)(x - 4)
= (x + 4)/(2x - 1)

2. (2x^2 + 14x + 24)/(4x + 4)
Factor numerator: 2(x^2 + 7x + 12)
Factor denominator: 4(x + 1)
= 2(x + 3)(x + 4)/4(x + 1)
= (x + 3)(x + 4)/(2(x + 1))

Now divide the two simplified fractions:
[x + 4 / (2x - 1)] ÷ [(x + 3)(x + 4) / (2(x + 1))]
= [x + 4 / (2x - 1)] * [(2(x + 1) / (x + 3)(x + 4)]
= [x + 4 / (2x - 1)] * [2 / (x + 3)]
= 2(x + 4) / (2x - 1)(x + 3)

Therefore, the correct option is: C: 2(x + 4) / (2x - 1)(x + 3)