What is m/(m-3)+(5m-48)/(m^2+5m-24) ?

The solution to m/(m-3)+(5m-48)/(m^2+5m-24) is (m+16)/(m+8)

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simplify m/(m-3)+(5m-48)/(m^2+5m-24)

simplify

\frac{m}{m - 3} + \frac{5 m - 48}{m ^{2} + 5 m - 24}

\frac{m + 16}{m + 8}

Solution steps

\frac{m}{m - 3} + \frac{5 m - 48}{m ^{2} + 5 m - 24}

Least Common Multiplier of

m - 3, m^{2} + 5 m - 24 : (m - 3) (m + 8)

Adjust Fractions based on the LCM

= \frac{m ( m + 8 )}{( m - 3 ) ( m + 8 )} + \frac{5 m - 48}{( m - 3 ) ( m + 8 )}

Apply the fraction rule:

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

= \frac{m ( m + 8 ) + 5 m - 48}{( m - 3 ) ( m + 8 )}

Simplify

m (m + 8) + 5 m - 48 : m^{2} + 13 m - 48

= \frac{m ^{2} + 13 m - 48}{( m - 3 ) ( m + 8 )}

Cancel

\frac{m ^{2} + 13 m - 48}{( m - 3 ) ( m + 8 )} : \frac{m + 16}{m + 8}

= \frac{m + 16}{m + 8}

9 x^{2} + x - 8 = 0

4^{∣ x ∣} = 128

5 u^{2} - 3 u + 2 = 0

\frac{2}{4} + \frac{3}{4}

5 x p + 5 x

What is m/(m-3)+(5m-48)/(m^2+5m-24) ?
The solution to m/(m-3)+(5m-48)/(m^2+5m-24) is (m+16)/(m+8)