How do you do this question?
I am not sure if this right.
1. solve rational equation
A) (x+3)/(x-1)=2x+1
x+3=(2x+1)(x-1)
x+3=2x^2 - 2x + x - 1
??
collect all like terms to get a quadratic equation
2x^2 - 3x - 4 = 0
use the formula to solve for x
So I have to use quadratic formula right? If so, no wonder I don't get the answer
I think I added the x terms up incorrectly
should have been
2x^2 - 2x -4 = 0
divide by 2
x^2 - x - 2 = 0
now it factors
x(-2)(x+1) = 0
x = 2 or x = -1
To solve the given rational equation (x+3)/(x-1) = 2x+1, you can follow these steps:
1. Multiply both sides of the equation by the denominator (x-1) to eliminate the fraction:
(x+3) * (x-1)/(x-1) = (2x+1) * (x-1)/(x-1)
Simplifying this equation results in:
x + 3 = 2x^2 - 2x + x - 1
2. Combine like terms on the right side of the equation:
x + 3 = 2x^2 - x - 1
3. Rearrange the equation so it is in standard quadratic form (ax^2 + bx + c = 0):
2x^2 - x - 1 - (x + 3) = 0
2x^2 - x - 1 - x - 3 = 0
2x^2 - 2x - 4 = 0
4. Set the equation equal to zero by subtracting the entire equation by the constant term (-4):
2x^2 - 2x - 4 - 0 = 0
Now you can proceed to solve this quadratic equation. You can factor it or use the quadratic formula to find the values of x. Once you find the values of x, you can check if they satisfy the original equation by substituting them back into the equation and verifying if both sides are equal.