What is (m^2)/(m^2-4)+1/(2-m) ?

The solution to (m^2)/(m^2-4)+1/(2-m) is (m+1)/(m+2)

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simplify (m^2)/(m^2-4)+1/(2-m)

simplify

\frac{m ^{2}}{m ^{2} - 4} + \frac{1}{2 - m}

\frac{m + 1}{m + 2}

Solution steps

\frac{m ^{2}}{m ^{2} - 4} + \frac{1}{2 - m}

Least Common Multiplier of

m^{2} - 4, 2 - m : (m + 2) (m - 2) (- m + 2)

Adjust Fractions based on the LCM

= \frac{m ^{2} ( - m + 2 )}{( m + 2 ) ( m - 2 ) ( - m + 2 )} + \frac{- ( m + 2 ) ( - m + 2 )}{( m + 2 ) ( m - 2 ) ( - m + 2 )}

Apply the fraction rule:

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

= \frac{m ^{2} ( - m + 2 ) - ( m + 2 ) ( - m + 2 )}{( m + 2 ) ( m - 2 ) ( - m + 2 )}

Simplify

m^{2} (- m + 2) - (m + 2) (- m + 2) : - m^{3} + 3 m^{2} - 4

= \frac{- m ^{3} + 3 m ^{2} - 4}{( m + 2 ) ( m - 2 ) ( - m + 2 )}

Cancel

\frac{- m ^{3} + 3 m ^{2} - 4}{( m + 2 ) ( m - 2 ) ( - m + 2 )} : \frac{m + 1}{m + 2}

= \frac{m + 1}{m + 2}

36 a^{3} b^{4} - 20 a^{2} b^{3} - 8 a b^{2}

\frac{1}{\frac{5}{7}}

\frac{6 - 3 i}{4 + 2 i}

2 x^{2} = 5 x

3 x^{2} = 5 x

What is (m^2)/(m^2-4)+1/(2-m) ?
The solution to (m^2)/(m^2-4)+1/(2-m) is (m+1)/(m+2)