What is (3x)/(2x+4)-(5-2x)/(x^2-4) ?

The solution to (3x)/(2x+4)-(5-2x)/(x^2-4) is (3x^2-2x-10)/(2(x+2)(x-2))

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simplify (3x)/(2x+4)-(5-2x)/(x^2-4)

simplify

\frac{3 x}{2 x + 4} - \frac{5 - 2 x}{x ^{2} - 4}

\frac{3 x ^{2} - 2 x - 10}{2 ( x + 2 ) ( x - 2 )}

Solution steps

\frac{3 x}{2 x + 4} - \frac{5 - 2 x}{x ^{2} - 4}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{3 x ( x - 2 )}{2 ( x + 2 ) ( x - 2 )} - \frac{( 5 - 2 x ) \cdot 2}{2 ( x + 2 ) ( x - 2 )}

Apply the fraction rule:

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

= \frac{3 x ( x - 2 ) - ( 5 - 2 x ) \cdot 2}{2 ( x + 2 ) ( x - 2 )}

Simplify

3 x (x - 2) - (5 - 2 x) \cdot 2 : 3 x^{2} - 2 x - 10

= \frac{3 x ^{2} - 2 x - 10}{2 ( x + 2 ) ( x - 2 )}

20 lo g_{10} (20)

(x - 3) (x^{2})

3 \times (- 5)

(3 x + 1) (x - 2)

216 v

What is (3x)/(2x+4)-(5-2x)/(x^2-4) ?
The solution to (3x)/(2x+4)-(5-2x)/(x^2-4) is (3x^2-2x-10)/(2(x+2)(x-2))