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