The domain is therefore the point where x > - 1 or x < -1 and the solution to the given equation is x = -1/2 and x = 3
Solving rational expression
Rational expressions are expressions written as a ratio of two expressions. Given the following expression;
x+3/x-1 + 2x-1/1-x = x-1/x+1
Find the LCM to have;
(x+3)(1-x)+(2x-1)(x-1)/(x-1)(1-x) = x-1/x+1
x-x^2+3-3x+2x^2-2x-x+1/(x-1)(1-x) = x-1/x+1
x^2-5x+4/(x-1)(1-x) = x-1/x+1
(x-1)(x-4)/(x-1)(1-x) = x-1/x+1
x-4/1-x = x-1/x+1
Cross multiply to have:
(x-4)(x+1) = (1-x)(x-1)
x^2 + x - 4x - 4 = x -1 - x^2 + x
x^2+x^2-4x-3-x = 0
2x^2-5x-3 = 0
2x^2-6x+x-3 = 0
2x(x-3)+1(x-3) = 0
2x+1= 0and x -3 = 0
x = -1/2 and x = 3
The domain is the value of the independent variable for which the expression exists
The domain is at the point where x > - 1 or x < -1
Learn more on domain of a function here: https://brainly.com/question/1369616
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