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
12z^2 - 7z -12/ 3z^2 + 2z - 8
= (4z+3) (3z -4)/ (z+2)(3z -4)
= (4z + 3) / (x+2)
Hope this helps
Answer: Simplified form is \(\frac{4z+3}{z+2}\)
Step-by-step explanation:
Since we have given that
\(\frac{12z^2-7z-12}{3z^2-2z-8}\)
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:
\(\frac{(4z+3)(3z-4)}{(z+2)(3z-4)}\\\\\text{Cancel out the common term i.e. 3z-4}\\\\=\frac{4z+3}{z+2}\)
Hence, simplified form is \(\frac{4z+3}{z+2}\)