Question

(Z^2-4z-21)/(z^2-6z-7)

Answer 1

$\frac{z^{2}-4z-21 }{z^{2}-6z-7 }=\frac{(z+3)(z-7)}{(z+1)(z-7)}=\frac{z+3}{z+1}\\\\Otvet:\boxed{\frac{z+3}{z+1}}$

Answer 2

To simplify the expression (z^2 - 4z - 21)/(z^2 - 6z - 7), we can factorize the numerator and denominator separately and then cancel out any common factors.

First, let's factorize the numerator:

z^2 - 4z - 21 = (z - 7)(z + 3)

Now, let's factorize the denominator:

z^2 - 6z - 7 = (z - 7)(z + 1)

Now, we can rewrite the expression as:

[(z - 7)(z + 3)] / [(z - 7)(z + 1)]

Next, we can cancel out the common factor (z - 7) from the numerator and denominator:

[(z - 7)(z + 3)] / [(z - 7)(z + 1)] = (z + 3) / (z + 1)

Therefore, the simplified expression is (z + 3) / (z + 1).