When graphing radical equations using shifts, adding or subtracting a constant that is not in the radical will shift the graph up (adding) or down (subtracting). Adding or subtracting a constant that is in the radical will shift the graph left (adding) or right (subtracting). Multiplying a negative constant by the equation will reflect the graph over the x-axis. Multiplying by a number larger than one increases the y-values.
Remember that solving an equation means that you're going to try to look for what the variable is equal to or what values of that variable makes your equation equality. Watch out for what we call excluded values, an excluded value is any value of the variable that would make your fraction undefined or that would make your denominator equal to zero. That's really important when you're solving rational equations. A lot of times you do all kinds of Mathy stuff and you get an answer you think you got it right but it turns out what you found was an excluded value. You always have to check at the end that your solution makes sense. Other things to be careful of are making sure you have common denominators when you're adding or subtracting fractions. The last thing is a shortcut, if ever all of your fractions have the exact same denominator or if you can multiply things such that they have the exact same denominator those denominators can be canceled out. It's the essentially you're multiplying all of those terms by the denominator so denominators go away, then you can just work with the tops. That's a great strategy to think about when you're solving equations involving rational expressions. One other strategy you always want to look out for is cross multiplying. If you have 2 equal fractions you can cross multiply and work through your equation that way. So good luck with this guys these are pretty difficult, they are pretty challenging but you can do it and a couple of strategies for you to keep in the back of your head are cross multiplying and clearing the denominators.
Experience the 'A-Ha!' moment with the best teachers
whom we hand-picked for you!
M.A. in Secondary Mathematics, Stanford University B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
“Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
“Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
“You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”