# Math

Some of the content of this guide was modeled after a guide originally created by the Openstax and has been adapted for the GPRC Learning Commons in September 2020. This work is licensed under a Creative Commons BY 4.0 International License. Rational Equations and Problem Solving

##### Step 1) The least common denominator for the denominators in this example is . Therefore, we multiply all the terms by : ##### Step 2) We simplify the equation from step 1: ##### Step 3) We solve for x: ##### Step 4) We verify the solution by substituting the solution into the original equation ##### Step 1) We have to multiply everything by the least common denominator. To do so, we have to factor denominators and find the least common denominator for them: ##### now, we substitute the factored form of the denominators into the original equation: ##### The least common denominator is . So, we multiply everything by the least common denominator: ##### Step 2) We simplify the above equation: ##### Step 3) We solve the equation from step 2: ##### Step 4) We verify the solution: ##### after simplifying, we get: 