What is the quotient
[(x^2) / (2x^2-9x + 4)] / [(2x^2 + 14x + 24) / (4x + 4)]
2x^2-9x+4 = (2x-1)(x-4)
2x^2+14x+24 = 2(x+4)(x+3)
so, what you have is
x^2 / (2x-1)(x-4) * 4(x+1) / 2(x+4)(x+3)
hm. no factors cancel but the 2's, so we wind up with
2x^2(x+1) / (2x-1)(x-4)(x+4)(x+3)
= (2x^3 + 2x^2)/(2x^4+5x^3-35x^2-80x+48)
Not very simple.
Steve, I am sorry, I left out a number:
What is the quotient?
[(x^2 -16) / (2x^2-9x + 4)] / [(2x^2 + 14x + 24) / (4x + 4)]
To find the quotient, we need to simplify the given expression. The expression is in the form of a fraction divided by another fraction. To divide fractions, we can multiply the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the numerator of the second fraction.
Let's start with the numerator:
[(x^2) / (2x^2-9x + 4)] * [(4x + 4) / (2x^2 + 14x + 24)]
Next, we'll simplify the numerator by multiplying the terms together:
[(x^2)(4x + 4)] / [(2x^2-9x + 4)(2x^2 + 14x + 24)]
Continuing to simplify, we can distribute the x^2 term:
[(4x^3 + 4x^2)] / [(2x^2-9x + 4)(2x^2 + 14x + 24)]
Now let's focus on the denominator:
(2x^2-9x + 4)(2x^2 + 14x + 24)
We can simplify this expression by multiplying each term of the first binomial by each term of the second binomial. The resulting expression becomes:
(4x^4 + 16x^3 - 18x^3 - 72x^2 + 20x^2 + 80x + 8x - 36 - 16)
Now, let's combine like terms and simplify further:
(4x^4 - 2x^3 + 22x^2 + 88x - 52)
Therefore, the simplified expression is:
(4x^3 + 4x^2) / (4x^4 - 2x^3 + 22x^2 + 88x - 52)