Solve 1 - (1/\epsilon ^(k-1)) * (\rho ^k - 1) / (k * (\rho - 1))

Evaluate

1 - (\frac{1}{ϵ ^{k - 1}}) \times \frac{ρ ^{k} - 1}{k ( ρ - 1 )}

Remove the unnecessary parentheses

1 - \frac{1}{ϵ ^{k - 1}} \times \frac{ρ ^{k} - 1}{k ( ρ - 1 )}

Multiply the terms

1 - \frac{ρ ^{k} - 1}{ϵ ^{k - 1} k ( ρ - 1 )}

Reduce fractions to a common denominator

\frac{ϵ ^{k - 1} k ( ρ - 1 )}{ϵ ^{k - 1} k ( ρ - 1 )} - \frac{ρ ^{k} - 1}{ϵ ^{k - 1} k ( ρ - 1 )}

Write all numerators above the common denominator

\frac{ϵ ^{k - 1} k ( ρ - 1 ) - ( ρ ^{k} - 1 )}{ϵ ^{k - 1} k ( ρ - 1 )}

Multiply the terms

More Steps

\frac{ρ ϵ ^{k - 1} k - k ϵ ^{k - 1} - ( ρ ^{k} - 1 )}{ϵ ^{k - 1} k ( ρ - 1 )}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

\frac{ρ ϵ ^{k - 1} k - k ϵ ^{k - 1} - ρ ^{k} + 1}{ϵ ^{k - 1} k ( ρ - 1 )}

Solution

More Steps

\frac{ρ ϵ ^{k - 1} k - k ϵ ^{k - 1} - ρ ^{k} + 1}{k ϵ ^{k - 1} ρ - k ϵ ^{k - 1}}

1 (1/\epsilon ^(k 1)) * (\rho ^k 1) / (k * (\rho 1))

Simplify the expression

Solution