How Do You Solve a Rational Equation by Adding Fractions?

Note:

Want some extra practice solving rational equations? This tutorial gives you just that! You'll see how to solve a rational equation containing rational expressions with common denominators. Then, you'll see how to solve an equation containing rational expressions with unlike denominators. Take a look!

Keywords:

problem
rational
rational expression
variable
variables
fraction
algebraic fraction
fractions
similar denominator
same denominator
add fractions
least common denominator
lcd
excluded value

Background Tutorials

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- How Do You Evaluate an Algebraic Expression?
  
  Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- What's a Proportion?
  
  The idea of proportions is that a ratio can be written in many ways and still be equal to the same value. That's why proportions are actually equations with equal ratios. This is a bit of a tricky definition, so make sure to watch the tutorial!
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
- How Do You Solve an Equation Using Division?
  
  Solving an equation for a variable? Perform the order of operations in reverse! Check it out in this tutorial.