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Least common denominator (z+z/q)*(z-z/q)

You have entered [src]

/    z\ /    z\
|z + -|*|z - -|
\    q/ \    q/

$$\left(z - \frac{z}{q}\right) \left(z + \frac{z}{q}\right)$$

(z + z/q)*(z - z/q)

General simplification [src]

$$z^{2} - \frac{z^{2}}{q^{2}}$$

z^2 - z^2/q^2

Common denominator [src]

$$z^{2} - \frac{z^{2}}{q^{2}}$$

z^2 - z^2/q^2

Rational denominator [src]

(z + q*z)*(-z + q*z)
--------------------
          2         
         q

$$\frac{\left(q z - z\right) \left(q z + z\right)}{q^{2}}$$

(z + q*z)*(-z + q*z)/q^2

Combinatorics [src]

 2                 
z *(1 + q)*(-1 + q)
-------------------
          2        
         q

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

z^2*(1 + q)*(-1 + q)/q^2

Numerical answer [src]

(z + z/q)*(z - z/q)

(z + z/q)*(z - z/q)

Combining rational expressions [src]

 2                 
z *(1 + q)*(-1 + q)
-------------------
          2        
         q

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

z^2*(1 + q)*(-1 + q)/q^2

Assemble expression [src]

 2 /    1\ /    1\
z *|1 + -|*|1 - -|
   \    q/ \    q/

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

z^2*(1 + 1/q)*(1 - 1/q)