What is a/(a^2-4)-1/(a-2) ?

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

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simplify a/(a^2-4)-1/(a-2)

simplify

\frac{a}{a ^{2} - 4} - \frac{1}{a - 2}

- \frac{2}{( a + 2 ) ( a - 2 )}

Solution steps

\frac{a}{a ^{2} - 4} - \frac{1}{a - 2}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

a - (a + 2) : - 2

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

Apply the fraction rule:

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

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

x^{2} + 5 x - 104

35 - 22 x + 6 - 18 x = 14 - 30 x + 32

6 x - 12 = 6 (x - 2)

6 m^{6} n + 7 m^{5} n^{2} + 2 m^{4} n^{3}

5 t^{2} + 3 t - 7 = 0

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