# Week 16 – Pre Calculus 11

Solving Rational Equations

To solve rational equations we must cancel out the denominators. To do this we must multiply by each denominator, this will cancel them out but because we have to do the same for everything in the equation, we will have then multiply the numerators by the values that were not canceled out. Before we do anything we must find the non-permissible values so we do not forget in the end.  If any of the solutions for x is a non-permissible value, it is extraneous and is not a real solution. To explain this we must show an example. The goal of the equation is to isolate and find x. We may have to solve a quadratic or linear equation to get x.

Here are the steps to solving a Rational Equation

1. Factor any quadratic functions you see in your equations
2. Multiply by the Denominator
3. Write down your non-permissible values
4. Solve

Example: $frac4k516k/33k212k36÷ frac 9k418k/34k24​$

Now the division looks as follows:
To divide two rational expressions, we “flip and multiply” and simplify
= $frac 4k3(k+2)(k2)3(k+2)(k6)⋅frac4(k6)9k3(k2)$
Next, Multiply across
= $frac4k3(k+2)(k2)⋅frac4(k6)3(k+2)(k6)9k3(k2)​$
The next step is to cancel out. When done you will be left with… $frac 27/16$
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