Answer: The simplified form of the given equation is \(\frac{2z+3}{z+3}\)
Step-by-step explanation:
From the given information, the numerator of the given fraction is: \(4z^2-4z-15\)
and denominator of the given fraction is \(2z^2+z-15\)
The fraction becomes:
\(\frac{4z^2-4z-15}{2z^2+z-15}\)
Applying middle term factorization in the numerator and denominator term, we get:
= \(\frac{4z^2-10z+6z-15}{2z^2+6z-5z-15}\)
= \(\frac{2z(2z-5)+3(2z-5)}{2z(z+3)-5(z+3)}\)
= \(\frac{(2z+3)(2z-5)}{(2z-5)(z+3)}\)
Cancelling (2z-5) factor from numerator an denominator, we get:
= \(\frac{2z+3}{z+3}\)
The above fraction is the simplified form of the equation formed in the question.
