Question

Solve the rational equation (3x^2+1)/(x-1) + x =4 + 4/(x-1)

A:X=1
B:X=1/4
C:There is no Solution
D:X=1/4, X=1

Answer 1

Answer is B: x=1/4

Explanation:

Answer 2

The answer to your question is letter D

Explanation:

Rational equation

`(3x^(2) + 1)/(x - 1) + x = 4 + (4)/(x - 1)`

Simplify

`(3x^(2) + 1 + x(x - 1))/(x - 1) = (4(x - 1) + 4)/(x - 1)`

Cancel the denominators and expand

3x² + 1 + x² - x = 4x - 4 + 4

Simplify

4x² - x + 1 - 4x = 0

4x² - 5x + 1 = 0

Factor

4x² - 4x - 1x + 1 = 0

4x(x - 1) - 1(x - 1) = 0

(4x - 1)(x - 1) = 0

x₁ = 1/4 x₂ = 1