Answer:
The answer should be:
[tex]=\frac{8x^3-18x}{3x+2}[/tex]
The closest answer is A, so I'll go with that.
Step-by-step explanation:
So we have the rational expression:
[tex]\frac{4x^3-9x}{2x-7}\div\frac{3x^2+2x^2}{4x^2-14x}[/tex]
First, remove the division sign. To do so, turn the division into multiplication and flip the second term:
[tex]\frac{4x^3-9x}{2x-7}\cdot \frac{4x^2-14x}{3x^2+2x}[/tex]
Now, simplify. From the first term, in the numerator, factor out a x. On the second term, factor out a 2x in the numerator and a x in the denominator:
[tex]\frac{x(4x^2-9)}{2x-7}\cdot\frac{2x(2x-7)}{x(3x+2)}[/tex]
Multiply straight across:
[tex]\frac{x(4x^2-9)(2x)(2x-7)}{(2x-7)(x)(3x+2)}[/tex]
Cancel out the (2x-7):
[tex]\frac{x(4x^2-9)(2x)}{x(3x+2)}[/tex]
Cancel out the x:
[tex]\frac{(2x)(4x^2-9)}{(3x+2)}[/tex]
At this point, we can factor the (4x^2-9) term, but we won't be able to cancel it out. Thus, this is the simplest it can get.
To get the answer, expand the numerator:
[tex]=\frac{8x^3-18x}{3x+2}[/tex]
Thus, the answer is...
A?
