What is 3/(2x+4)+(x-1)/(2x-4)+(x+8)/(x^2-4) ?

The solution to 3/(2x+4)+(x-1)/(2x-4)+(x+8)/(x^2-4) is (x+4)/(2(x-2))

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simplify 3/(2x+4)+(x-1)/(2x-4)+(x+8)/(x^2-4)

simplify

\frac{3}{2 x + 4} + \frac{x - 1}{2 x - 4} + \frac{x + 8}{x ^{2} - 4}

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

Solution steps

\frac{3}{2 x + 4} + \frac{x - 1}{2 x - 4} + \frac{x + 8}{x ^{2} - 4}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{3 ( x - 2 )}{2 ( x + 2 ) ( x - 2 )} + \frac{( x - 1 ) ( x + 2 )}{2 ( x + 2 ) ( x - 2 )} + \frac{( x + 8 ) \cdot 2}{2 ( x + 2 ) ( x - 2 )}

Apply the fraction rule:

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

= \frac{3 ( x - 2 ) + ( x - 1 ) ( x + 2 ) + ( x + 8 ) \cdot 2}{2 ( x + 2 ) ( x - 2 )}

Simplify

3 (x - 2) + (x - 1) (x + 2) + (x + 8) \cdot 2 : x^{2} + 6 x + 8

= \frac{x ^{2} + 6 x + 8}{2 ( x + 2 ) ( x - 2 )}

Cancel

\frac{x ^{2} + 6 x + 8}{2 ( x + 2 ) ( x - 2 )} : \frac{x + 4}{2 ( x - 2 )}

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

- 4 x + 5 x

(3 + 4 i) - (2 - i)

(x^{2} + 9) (x^{2} - 9)

6 - 6

9 + 4

What is 3/(2x+4)+(x-1)/(2x-4)+(x+8)/(x^2-4) ?
The solution to 3/(2x+4)+(x-1)/(2x-4)+(x+8)/(x^2-4) is (x+4)/(2(x-2))