Question

How do you simplify `\frac { x ^ { 2} - 4} { 3x ^ { 2} + 6x } \div \frac { 1} { 9x ^ { 2} }`?

Answer 1

see explanation

Explanation:

First re-write in a form that aids simplification. I factored both the numerator & denominator of the first term, and the denominator of the second term (the divisor:)

And then treat the division as a multiplication (by the INVERSE of the second term)

...so you can rewrite your given formula as:

`((x+2)(x-2))/(3x(x+2)) * ((3x)(3x))/1`

...you now have a `3x` and `(x+2)` factor that can be cancelled out.

...leaving you with:

`(x-2)(3x)`

which you can also write as:

`3x^2-6x`

GOOD LUCK

Answer 2

`=3x(x-2)`

Explanation:

first, use the rule of fractions for division: invert the second fraction and change to multiply

`(x^2-4)/(3x^2+6x)xx(9x^2)/1`

now factorise we shall it step by step

difference of squares in the numerator

`(color(blue)((x+2)(x-2)))/(3x^2+6x)xx(9x^2)/1`

common factors in the denominator

`((x+2)(x-2))/color(blue)(3x(x+2))xx(9x^2)/1`

now cancel out terms

`(cancel(color(blue)((x+2)))(x-2))/(cancel(3x)cancel(color(blue)((x+2))))xx(cancel(9x^2)^(3x))/1`

`=3x(x-2)`