Key Vocabs:

Non-permissible values: Values of the variable(s) that make the denominator of a rational expression equal to zero

Monomial: A polynomial with 1 term (ex. )

Binomial: A polynomial with 2 terms (ex. )

Trinomial: A polynomial with 3 terms (ex. )

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Moving on from addition, subtraction, multiplication, and dividing rational expressions, we began to solve rational equations. It’s important to know how we can solve these as we can connect the different knowledge gained from this unit into practice. It’s also important when we’re solving word problems. In a word problem, we are often given to answer the unknown, and so, knowing solving rational equations are essential.

Solving rational equations with monomial denominators:

ex1) + =

• Our first step is to find our non-permissible values because this will be helpful in finding our final solution of the equation
• Then we find the common denominator
• And start multiplying

• Since is a permissible value, it is our solution

Solving rational equation with binomial denominators:

ex2) =

• Just like the monomial procedures, we first find our non-permissible values
• Then find the common denominator
• And start multiplying

• Since is a permissible value, it the the solution

Solving rational equation with trinomial denominators:

ex3) = {-6}{x^2 – 8x +15}$

• Trinomial denominators, have an extra step if there is something to factor
• If a denominator is factorable, than factor it to find our non-permissible values
• Then we find our common denominator
• And do the same step as the monomial and binomial denominators