What is 5/m+(7m-5)/(m-2) ?

The solution to 5/m+(7m-5)/(m-2) is (7m^2-10)/(m(m-2))

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simplify 5/m+(7m-5)/(m-2)

simplify

\frac{5}{m} + \frac{7 m - 5}{m - 2}

\frac{7 m ^{2} - 10}{m ( m - 2 )}

Solution steps

\frac{5}{m} + \frac{7 m - 5}{m - 2}

Least Common Multiplier of

m, m - 2 : m (m - 2)

Adjust Fractions based on the LCM

= \frac{5 ( m - 2 )}{m ( m - 2 )} + \frac{( 7 m - 5 ) m}{m ( m - 2 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{5 ( m - 2 ) + ( 7 m - 5 ) m}{m ( m - 2 )}

Simplify

5 (m - 2) + (7 m - 5) m : 7 m^{2} - 10

= \frac{7 m ^{2} - 10}{m ( m - 2 )}

\frac{a ^{2} - 1}{3 a + 3}

\frac{144}{16}

3 b^{2} (- 4 b^{2} - 2 b + 4)

a \times a \times b \times b

\frac{12}{16}

What is 5/m+(7m-5)/(m-2) ?
The solution to 5/m+(7m-5)/(m-2) is (7m^2-10)/(m(m-2))