- #1
Mathnomalous
- 83
- 5
Homework Statement
Solve for x.
Homework Equations
3/2 + 2/2x-4 = 1/x-2
The Attempt at a Solution
LCD = 2(x-2)
3/2 + 2/2x-4 = 1/x-2 Mult. all terms by 2(x-2)
3x - 6 + 2 = 2
3x = 6
x = 2
What am I missing here?
A rational equation is an equation that contains rational expressions, which are fractions with variables in the numerator and/or denominator. These types of equations can be solved by clearing fractions and solving for the variable.
To solve a rational equation, you first need to clear the fractions by multiplying both sides of the equation by the least common denominator (LCD). Then, you can solve for the variable by following the same steps as solving a linear equation.
Yes, there may be restrictions when solving rational equations. These restrictions occur when the LCD contains variables, which would make the denominator equal to zero. In these cases, the value of the variable that makes the denominator zero is not a valid solution.
Yes, you can check your solution for a rational equation by plugging it back into the original equation and simplifying. If the resulting equation is true, then your solution is correct.
Yes, you can solve a rational equation with more than one variable by following the same steps as solving a single variable rational equation. However, you may need to use algebraic techniques such as substitution or elimination to solve for the variables.