Question

What is the simplified form of the quantity 12 z–squared minus 7z minus 12 over the quantity 3 z–squared plus 2z minus 8

Answer 1

Answer: Simplified form is
`(4z+3)/(z+2)`

Explanation:

Since we have given that

`(12z^2-7z-12)/(3z^2-2z-8)`

We need to simplify the above expression:

1) First we split the numerator :

`12z^2-7z-12=0\\\\12z^2-16z+9z-12=0\\\\4z(3z-4)+3(3z-4)=0\\\\(4z+3)(3z-4)=0`

Now,

2) we will split the denominator:

`3z^2+2z-8=0\\\\3z^2+6z-4z-8=0\\\\3z(z+2)-4(z+2)=0\\\\(3z-4)(z+2)=0`

Now, we will rewrite numerator and denominator in fraction form:

`((4z+3)(3z-4))/((z+2)(3z-4))\\\\\text{Cancel out the common term i.e. 3z-4}\\\\=(4z+3)/(z+2)`

Hence, simplified form is
`(4z+3)/(z+2)`

Answer 2

12z^2 - 7z -12/ 3z^2 + 2z - 8

= (4z+3) (3z -4)/ (z+2)(3z -4)

= (4z + 3) / (x+2)

Hope this helps