To simplify the expression (a/(a-1) + 1) / (1 - 3a^2)/(1-a^2), first find the LCD (lowest common denominator) for the fractions inside and outside the parentheses.
Inside the parentheses: a/(a-1) + 1 = a/(a-1) + (a-1)/(a-1) = (a + a - 1)/(a-1) = (2a - 1)/(a-1)
Outside the parentheses: 1 - 3a^2 = 1 - 3a^2.
Now simplify the expression: (2a - 1)/(a-1) / (1 - 3a^2)/(1-a^2)
To simplify the expression (a/(a-1) + 1) / (1 - 3a^2)/(1-a^2), first find the LCD (lowest common denominator) for the fractions inside and outside the parentheses.
Inside the parentheses:
a/(a-1) + 1 = a/(a-1) + (a-1)/(a-1)
= (a + a - 1)/(a-1) = (2a - 1)/(a-1)
Outside the parentheses:
1 - 3a^2 = 1 - 3a^2.
Now simplify the expression: (2a - 1)/(a-1) / (1 - 3a^2)/(1-a^2)
= (2a - 1)(1 - a^2) / (a-1)(1 - 3a^2)
= (2a - 1)(1 - a)(1 + a) / (a-1)(1 - a)(1 + a)
= (2a - 1) / (a-1)
So the simplified expression of (a/(a-1) + 1) / (1 - 3a^2)/(1-a^2) is (2a - 1) / (a-1)