Dividing Rational Expressions

[XxBubbleGummxX]

I need to simplify and state all the non permissible values for this equation:

4x^2-1/x+2 divide by 4x^2+2x/8x^2-32

 

[stapel]

I need to simplify and state all the non permissible values for this equation:

4x^2-1/x+2 divide by 4x^2+2x/8x^2-32

You can learn how to simplify and determine the domains here. You can learn how to divide rational expressions here.

Once you have learned the basic terms and techniques, please attempt the exercise. If you get stuck, you can then reply with a clear listing of what you've tried, at which point we can begin to help you get un-stuck. Thank you!

 

[Quaid]

(4x^2-1)/(x+2) divided by (4x^2+2x)/(8x^2-32)

The notation in blue above is just fine, for showing a compound ratio (i.e., one ratio divided by another).

But, you still need to text the grouping symbols around numerators and denominators. Or, you could use different colors, to show clearly what's on top versus bottom, but it's easier to just type the parentheses.

Please show us your factorizations (with proper grouping symbols).

Do you remember this rule?

(A/B)/(C/D) = (A/B)*(D/C)

In other words, dividing by a ratio is the same as multiplying by that ratio's reciprocal.

 

[XxBubbleGummxX]

This is what I got when I factored the equation:

(4x^2-1)/(x+2) divided by 2(2x^2+x)/2(4x^2-16)

 

[stapel]

This is what I got when I factored the equation:

(4x^2-1)/(x+2) divided by 2(2x^2+x)/2(4x^2-16)

Okay, so the first step is to learn how to factor polynomial expressions.

To learn how to factor the \(\displaystyle 4x^2\, +\, 2x\) (which is simple factoring), try here.

To learn how to factor the \(\displaystyle 4x^2\, -\, 1\) (which is a difference of squares), try here.

To factor the \(\displaystyle 8x^2\, -\, 3x\), first apply what you learned at the first link to take the common factor out front; then apply what you learned in the second link to factor the difference of squares.

If you get stuck, or if you're unsure of your result, please reply showing all of your steps. Thank you!