Solve z-6/z-1z+1/z+4

$$\frac{ z-6 }{ z-1 } \frac{ z+1 }{ z+4 }$$

Evaluate

$$\frac{\left(z-6\right)\left(z+1\right)}{\left(z-1\right)\left(z+4\right)}$$

Short Solution Steps

Multiply \frac{z-6}{z-1} times \frac{z+1}{z+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z-6\right)\left(z+1\right)}{\left(z-1\right)\left(z+4\right)}$$

Apply the distributive property by multiplying each term of z-6 by each term of z+1.

$$\frac{z^{2}+z-6z-6}{\left(z-1\right)\left(z+4\right)}$$

Combine z and -6z to get -5z.

$$\frac{z^{2}-5z-6}{\left(z-1\right)\left(z+4\right)}$$

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

$$\frac{z^{2}-5z-6}{z^{2}+4z-z-4}$$

Combine 4z and -z to get 3z.

$$\frac{z^{2}-5z-6}{z^{2}+3z-4}$$

Expand

$$\frac{z^{2}-5z-6}{\left(z-1\right)\left(z+4\right)}$$

Short Solution Steps

Multiply \frac{z-6}{z-1} times \frac{z+1}{z+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(z-6\right)\left(z+1\right)}{\left(z-1\right)\left(z+4\right)}$$

Apply the distributive property by multiplying each term of z-6 by each term of z+1.

$$\frac{z^{2}+z-6z-6}{\left(z-1\right)\left(z+4\right)}$$

Combine z and -6z to get -5z.

$$\frac{z^{2}-5z-6}{\left(z-1\right)\left(z+4\right)}$$

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

$$\frac{z^{2}-5z-6}{z^{2}+4z-z-4}$$

Combine 4z and -z to get 3z.

$$\frac{z^{2}-5z-6}{z^{2}+3z-4}$$