Final answer:
The student is solving an equation with rational expressions. They need to combine the fractions on the left, use the common denominator, and then solve for x. Factoring, simplification, and rational expression manipulation are involved.
Step-by-step explanation:
The student is asking to solve the equation involving rational expressions:
-(3)/(x-1) + (5)/(x-3) = -(1)/(x^2-4x+3).
First, recognize that the denominator of the right-hand side of the equation, x^2-4x+3, can be factored:
x^2 - 4x + 3 = (x - 1)(x - 3).
Then notice that the denominators of the fractions on the left-hand side of the equation match the factors of the right-hand side's denominator. So you can combine the two fractions on the left-hand side over a common denominator:
-3/(x-1) + 5/(x-3) = (-3)(x - 3) + (5)(x - 1) / (x - 1)(x - 3).
Now cancel out the common term, (x - 1)(x - 3), on both sides of the equation:
(-3)(x - 3) + (5)(x - 1) = -1.
Solve the equation from this point to find the value of x.