What is ((3x))/((x^2-4))+4/((x-2)) ?

The solution to ((3x))/((x^2-4))+4/((x-2)) is (7x+8)/((x+2)(x-2))

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simplify ((3x))/((x^2-4))+4/((x-2))

simplify

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

\frac{7 x + 8}{( x + 2 ) ( x - 2 )}

Solution steps

\frac{3 x}{x ^{2} - 4} + \frac{4}{x - 2}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

3 x + 4 (x + 2) : 7 x + 8

= \frac{7 x + 8}{( x + 2 ) ( x - 2 )}

\frac{( x ^{2} - 8 )}{( x ^{4} )}

(m + k) (2 m - k) (m + k)

\frac{( - 2 x + 5 x - 10 + 4 )}{( 10 )}

(x + 2) 22 x^{2}

(\frac{3 x}{2}) - (\frac{( x - 2 )}{3})

What is ((3x))/((x^2-4))+4/((x-2)) ?
The solution to ((3x))/((x^2-4))+4/((x-2)) is (7x+8)/((x+2)(x-2))