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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 (a + 1)^{2} - (a + 2) a : a^{2} + 2 a + 2

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

- 5 x + 8 \leq 23

\frac{y ^{\frac{2}{7}}}{y ^{\frac{2}{3}}}

\frac{r}{5} > 2

- 8 < 7 - 5 x \leq 127

3 \leq 2 x - 1 \leq 9

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