Solve m + (m/(k-1)) + (m-1)/(k-1) * (k-2)/m * k

Question

Simplify the expression

\frac{m ^{2} k + m k ^{2} - 2 mk - k ^{2} + 2 k}{mk - m}

Evaluate

m + (\frac{m}{k - 1}) + \frac{m - 1}{k - 1} \times \frac{k - 2}{m} \times k

Remove the unnecessary parentheses

m + \frac{m}{k - 1} + \frac{m - 1}{k - 1} \times \frac{k - 2}{m} \times k

Multiply the terms

More Steps

m + \frac{m}{k - 1} + \frac{( m - 1 ) ( k - 2 ) k}{m ( k - 1 )}

Reduce fractions to a common denominator

\frac{m ( k - 1 ) m}{( k - 1 ) m} + \frac{m \times m}{( k - 1 ) m} + \frac{( m - 1 ) ( k - 2 ) k}{m ( k - 1 )}

Rewrite the expression

\frac{m ( k - 1 ) m}{m ( k - 1 )} + \frac{m \times m}{m ( k - 1 )} + \frac{( m - 1 ) ( k - 2 ) k}{m ( k - 1 )}

Write all numerators above the common denominator

\frac{m ( k - 1 ) m + m \times m + ( m - 1 ) ( k - 2 ) k}{m ( k - 1 )}

Multiply the terms

More Steps

\frac{m ^{2} k - m ^{2} + m \times m + ( m - 1 ) ( k - 2 ) k}{m ( k - 1 )}

Multiply the terms

\frac{m ^{2} k - m ^{2} + m ^{2} + ( m - 1 ) ( k - 2 ) k}{m ( k - 1 )}

Multiply the terms

More Steps

\frac{m ^{2} k - m ^{2} + m ^{2} + m k ^{2} - 2 mk - k ^{2} + 2 k}{m ( k - 1 )}

Calculate the sum or difference

More Steps

\frac{m ^{2} k + m k ^{2} - 2 mk - k ^{2} + 2 k}{m ( k - 1 )}

Solution

More Steps

\frac{m ^{2} k + m k ^{2} - 2 mk - k ^{2} + 2 k}{mk - m}

Show Solution

k = 1, m = 0

Show Solution