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Solving a Rational Equation for a parameter - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Solving rational equations is substantially easier with like denominators. When solving equations with rational numbers, we first multiply every term in the equation by the common denominator so the equation is "cleared" of fractions. Next, we use an appropriate technique for solving for the variable, such as isolating and simplifying.

Solving a rational equation for a parameter is pretty much exactly same as solving it for a variable except the parameter is typically in a application where we're dealing with a lot more variables so how we solve it is going to be the exact same as we solve anything else? First thing we want to do is to get rid of our denominator which is basically need to multiply through by the least common denominator.
For this one we have a fraction equal the fraction it's basically the same thing as cross multiplying but just to keep it all by the book what I want to do is multiply by my least common denominator which is just going to be capital T lower case t in this instance, so for the first term my capital T's cancel leaving me with little t capital P capital V is equal to capital T lower case pv because my little t's cancel. Alright so then we're just solving for little t divide by the coefficient p and v are variables but they are just numbers they're just representing numbers so we can just divide by them just like we could anything else, so we divide and we end up with little t is equal to capital T little pv over big PV they're all just variables you treat them as we would any other number and that is how we solve a rational equation for a parameter.

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