To solve this equation, we first need to find a common denominator for the fractions on the left side of the equation.
First fraction1 / (x^2 - 1)
Second fraction2 / (x^2 - 1)
So, the common denominator is (x^2 - 1).
Now, we rewrite the fractions with the common denominator:
(1) / (x^2 - 1) - (2) / (x^2 - 1) = 1 / (x - 1)
Now, combine the fractions:
(1 - 2) / (x^2 - 1) = 1 / (x - 1)
-1 / (x^2 - 1) = 1 / (x - 1)
Now, cross multiply:
Expand both sides:
Rearrange the equation:
x^2 + x - 2 = 0
Now, solve the quadratic equation for x:
x = (-1 ± √(1 + 8)) / 2
x = (-1 ± √9) / 2
x = (-1 ± 3) / 2
x = -4 / 2 = -2 or x = 2 / 2 = 1
Therefore, the values of x that satisfy the equation are x = -2 and x = 1.
To solve this equation, we first need to find a common denominator for the fractions on the left side of the equation.
First fraction
1 / (x^2 - 1)
Second fraction
2 / (x^2 - 1)
So, the common denominator is (x^2 - 1).
Now, we rewrite the fractions with the common denominator:
(1) / (x^2 - 1) - (2) / (x^2 - 1) = 1 / (x - 1)
Now, combine the fractions:
(1 - 2) / (x^2 - 1) = 1 / (x - 1)
-1 / (x^2 - 1) = 1 / (x - 1)
Now, cross multiply:
(x - 1) = (x^2 - 1)Expand both sides:
x + 1 = x^2 - 1Rearrange the equation:
x^2 + x - 2 = 0
Now, solve the quadratic equation for x:
x = (-1 ± √(1 + 8)) / 2
x = (-1 ± √9) / 2
x = (-1 ± 3) / 2
x = -4 / 2 = -2 or x = 2 / 2 = 1
Therefore, the values of x that satisfy the equation are x = -2 and x = 1.