Rational Expressions
A rational expression is when there are polynomials in the numerator and denominator. These need to be simplified and some values are not permitted.
Find non-permissible values
y = 12/(x^2 -4)
Find non-permissible values
y = (-9x+8)/(-9x^2 -55x +56)
Simplify ...
(6a^4b^7)/(3ab)^2 x (a^4b^7)/(3ab^4)^3
Simplify (+ powers only)
[(4x^8y^5)(2xy)^3]/[(x^8y^5)^3/(2xy^8)^4 ]
Simplify (again!)
This is a product and division. See thumbnail for description.
Is Simplify (with division)
This one has another step yet. See thumbnail for description.
Simplify (the sum)
You'll need to find a common denominator before you add these rational expressions.
More complex
This one has layers and layers of division. Simplify and find the non-permissible values.
Do this one in your head!
33 + 33/5 + 33/25 ... Is this convergent or divergent, and does it have a sum?
Word Problem - Road Trip!
Two girls are planning a 60 km road trip. For the first half of the trip they travel at speed "x". Then they increase to x+5 km/hr. Find the total time. Simplify!
Simplify (messy)
Check out this problem with division of expressions. It involves a lot of factoring.
More factoring.
Factoring and common denominator - you'll need both to subtract these two.
And now there are 3!
It gets more complicated as we have 3 terms to add. And don't forget to simplify.
Equivalence ...
What does it mean for rational expressions to be equivalent? Stick around to find out. We'll do two different examples.
Equivalence & operations
The final problem in this set is not easy. It will require various operations with two different function (rational expressions). Good luck!