To solve this equation, we first need to find a common denominator on the left side of the equation.
The common denominator for the fractions on the left side would be (x-3)(x-1). Multiplying each fraction by the necessary factors to achieve this common denominator, we get:
To solve this equation, we first need to find a common denominator on the left side of the equation.
The common denominator for the fractions on the left side would be (x-3)(x-1). Multiplying each fraction by the necessary factors to achieve this common denominator, we get:
10(x-1)/(x-3)(x-1) + (3x-6)(x-3)/(x-3)(x-1) = 3/(x-3)(x-1)
Now, combine the fractions on the left side:
(10x-10 + 3x^2 - 9x)/(x-3)(x-1) = 3/(x-3)(x-1)
Simplify the numerator:
(3x^2 + x - 10)/(x-3)(x-1) = 3/(x-3)(x-1)
Now, multiply both sides by (x-3)(x-1) to get rid of the denominators:
3x^2 + x - 10 = 3
Rearrange the equation:
3x^2 + x - 13 = 0
Now, solve for x. You can do this by factoring the quadratic equation or using the quadratic formula:
x = (-1 ± √(1 + 4313)) / (2*3
x = (-1 ± √(1 + 156)) /
x = (-1 ± √157) / 6
So the solutions to the equation are:
x = (-1 + √157) / 6 and x = (-1 - √157) / 6