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

The solution to (a-2)/(a^2-3a+4)-(a-1)/(a^2-a-2) is (a^2-7a+8)/((a+1)(a-2)(a^2-3a+4))

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simplify (a-2)/(a^2-3a+4)-(a-1)/(a^2-a-2)

simplify

\frac{a - 2}{a ^{2} - 3 a + 4} - \frac{a - 1}{a ^{2} - a - 2}

\frac{a ^{2} - 7 a + 8}{( a + 1 ) ( a - 2 ) ( a ^{2} - 3 a + 4 )}

Solution steps

\frac{a - 2}{a ^{2} - 3 a + 4} - \frac{a - 1}{a ^{2} - a - 2}

Least Common Multiplier of

a^{2} - 3 a + 4, a^{2} - a - 2 : (a + 1) (a - 2) (a^{2} - 3 a + 4)

Adjust Fractions based on the LCM

= \frac{( a + 1 ) ( a - 2 ) ^{2}}{( a + 1 ) ( a - 2 ) ( a ^{2} - 3 a + 4 )} - \frac{( a - 1 ) ( a ^{2} - 3 a + 4 )}{( a + 1 ) ( a - 2 ) ( a ^{2} - 3 a + 4 )}

Apply the fraction rule:

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

= \frac{( a + 1 ) ( a - 2 ) ^{2} - ( a - 1 ) ( a ^{2} - 3 a + 4 )}{( a + 1 ) ( a - 2 ) ( a ^{2} - 3 a + 4 )}

Simplify

(a + 1) (a - 2)^{2} - (a - 1) (a^{2} - 3 a + 4) : a^{2} - 7 a + 8

= \frac{a ^{2} - 7 a + 8}{( a + 1 ) ( a - 2 ) ( a ^{2} - 3 a + 4 )}

y^{2} z^{2} - 16

(\frac{5}{4})^{- 4}

∣ x + 7 ∣ \leq 9

- \frac{1}{2} (- 2)

2 x + 4 = 0

What is (a-2)/(a^2-3a+4)-(a-1)/(a^2-a-2) ?
The solution to (a-2)/(a^2-3a+4)-(a-1)/(a^2-a-2) is (a^2-7a+8)/((a+1)(a-2)(a^2-3a+4))