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

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

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

simplify

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

\frac{1}{x ( x + 2 )}

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{( x + 4 ) x}{x ( x + 2 ) ( x - 2 )} - \frac{( x + 1 ) ( x + 2 )}{x ( x + 2 ) ( x - 2 )}

Apply the fraction rule:

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

= \frac{( x + 4 ) x - ( x + 1 ) ( x + 2 )}{x ( x + 2 ) ( x - 2 )}

Simplify

(x + 4) x - (x + 1) (x + 2) : x - 2

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

Cancel the common factor:

x - 2

= \frac{1}{x ( x + 2 )}

- \frac{4}{7 - 6 i}

\frac{7}{x ^{2} - 5 x - 24} - \frac{2}{x + 3}

(9 x + 5) (- 4 x - 8 + 10 x^{2})

0.1 3^{2}

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