how do I simplify this fraction?

Question

3x^3 +x^2 -2x
____________
9x^2 - 4

Answer 1

You have a difference of squares in the denominator, and a common x in the numerator, so factor those out...

x(3x² + x - 2)
-------------------
(3x - 2)(3x + 2)

Now factor the numerator. Intuition tells me that 3x - 2 or 3x + 2 will be a factor. In fact if you try it, you see that 3x - 2 is a factor, leaving:
x (3x - 2)(x + 1)
-------------------
(3x - 2)(3x + 2)

Now 3x - 2 cancels out:
x(x + 1)
----------
3x + 2

There is your simplified fraction

Answer 2

3x^3 +x^2 -2x/9x^2 - 4

step 1: factor out the x from the numerator
x(3x^2 + x -2) / 9x^2 - 4
step 2: factor the numerator
x(x+1)(3x-2) / 9x^2 - 4
step 3: factor the denominator
x(x+1)(3x-2) / (3x-2)(3x+2)
step 4: cancel out the (3x-2) from the numerator and denominator
x(x+1)/(3x+2)

there's your answer in simplest form

Answer 3

First, you need to factor the top and bottom sections into simplier forms (if possible). Then you can see if any of these factors are in common between the numerator (top) and denominator (bottom).

Try factoring the numerator first. Is there a common factor that can easily be brought out in front?

Then try factoring the denominator.

Good Luck with the rest of your homework :).

Answer 4

3x^3 + x^2 – 2x
____________ factorize numerator and denominator
9x^2 – 4

x(3x – 2)(x + 1) divide by 3x - 2
____________
(3x + 2)(3x – 2)

= x(x + 1)
____________
3x + 2

Answer 5

i think Mr Okupe is right