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

The solution to (a-1)/(a-2)-(a-2)/(a+3)+1/(a-1) is (7a^2-12a+1)/((a-2)(a+3)(a-1))

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

simplify

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

\frac{7 a ^{2} - 12 a + 1}{( a - 2 ) ( a + 3 ) ( a - 1 )}

Solution steps

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

Least Common Multiplier of

a - 2, a + 3, a - 1 : (a - 2) (a + 3) (a - 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(a + 3) (a - 1)^{2} - (a - 2)^{2} (a - 1) + (a - 2) (a + 3) : 7 a^{2} - 12 a + 1

= \frac{7 a ^{2} - 12 a + 1}{( a - 2 ) ( a + 3 ) ( a - 1 )}

(3 x - 2 y)^{4}

45 p^{2}

(12 x^{2} - 8 x - 15) m^{2}

(x^{- 1})^{- 1}

\frac{( n + 1 ) !}{( n - 1 ) !}

What is (a-1)/(a-2)-(a-2)/(a+3)+1/(a-1) ?
The solution to (a-1)/(a-2)-(a-2)/(a+3)+1/(a-1) is (7a^2-12a+1)/((a-2)(a+3)(a-1))