Solve (z-b)/(z-1)*(z+1)/(z+4)

$$\frac { ( z - b ) } { ( z - 1 ) } \cdot \frac { ( z + 1 ) } { ( z + 4 ) }$$

Evaluate

$$\frac{\left(z+1\right)\left(z-b\right)}{\left(z-1\right)\left(z+4\right)}$$

Short Solution Steps

Multiply \frac{z-b}{z-1} times \frac{z+1}{z+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z-b\right)\left(z+1\right)}{\left(z-1\right)\left(z+4\right)}$$

Apply the distributive property by multiplying each term of z-b by each term of z+1.

$$\frac{z^{2}+z-bz-b}{\left(z-1\right)\left(z+4\right)}$$

Apply the distributive property by multiplying each term of z-1 by each term of z+4.

$$\frac{z^{2}+z-bz-b}{z^{2}+4z-z-4}$$

Combine 4z and -z to get 3z.

$$\frac{z^{2}+z-bz-b}{z^{2}+3z-4}$$

Expand

$$\frac{z^{2}-bz+z-b}{\left(z-1\right)\left(z+4\right)}$$

Short Solution Steps

Multiply \frac{z-b}{z-1} times \frac{z+1}{z+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z-b\right)\left(z+1\right)}{\left(z-1\right)\left(z+4\right)}$$

Apply the distributive property by multiplying each term of z-b by each term of z+1.

$$\frac{z^{2}+z-bz-b}{\left(z-1\right)\left(z+4\right)}$$

Apply the distributive property by multiplying each term of z-1 by each term of z+4.

$$\frac{z^{2}+z-bz-b}{z^{2}+4z-z-4}$$

Combine 4z and -z to get 3z.

$$\frac{z^{2}+z-bz-b}{z^{2}+3z-4}$$