What is (2x)/(x+4)-(x^2+4)/(x^2-16) ?

The solution to (2x)/(x+4)-(x^2+4)/(x^2-16) is (x^2-8x-4)/((x+4)(x-4))

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simplify (2x)/(x+4)-(x^2+4)/(x^2-16)

simplify

\frac{2 x}{x + 4} - \frac{x ^{2} + 4}{x ^{2} - 16}

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

Solution steps

\frac{2 x}{x + 4} - \frac{x ^{2} + 4}{x ^{2} - 16}

Least Common Multiplier of

x + 4, x^{2} - 16 : (x + 4) (x - 4)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

(- 3 x^{2}) (3 x^{5})

19 + (- 12)

4 lo g_{9} (3) + 2 lo g_{9} (3)

\frac{5 2}{3}

\frac{2 a ^{2}}{3 b} \times \frac{6 b ^{2}}{4 a}

What is (2x)/(x+4)-(x^2+4)/(x^2-16) ?
The solution to (2x)/(x+4)-(x^2+4)/(x^2-16) is (x^2-8x-4)/((x+4)(x-4))