Solving Rational Equations

www.greenemath....
/ mathematicsbyjgreene
In this lesson, we review solving rational equations. To solve a rational equation, we will multiply both sides by the LCD of all rational expressions. We must be careful, since multiplying both sides by a variable or variable expression will sometimes give us extraneous solutions. Therefore, we must always check our proposed solutions for a rational equation in the original equation.

[@mikerich8661]

Whenever I solve a rational equation, when using the zero product property, if a factor matches with at least one of the denominators of the original rational equation, I underline it to show that this factor can be ignored because it would have a value that is not permissible in the original rational equation. For example if (x + 7) is in one of the denominator at least and is in the equation (x + 7)(x - 8) = 0, I would underline the (x + 7) and ignore it because it would cause an extraneous solution to the original rational equation. Hope this explains how I solve rational equations.

[@Greenemath]

Some books will show it that way as well by putting the domain out first. {x | x ≠ -7, 8}

[@adelinamarasigan2147]

Thank u so much. God bless!

[@Greenemath]

You are so welcome! Good luck with your studies :)

[@reydichos8560]

in the first example. where do you get the "add 10" and the "-2" pls comment hehe

[@Greenemath]

What's the time marker?

[@reydichos8560]

3:49

[@Greenemath]

@@reydichos8560 In order to solve the equation for x, you need x by itself on one side. 2x - 10 = x + 4, so to get rid of the 10, we add 10 to both sides.
2x - 10 + 10 = x + 4 + 10
The -10 + 10 becomes 0, so you just have 2x on the left.
2x = x + 14
So from there, you can subtract x away from each side:
2x - x = x - x + 14
x = 14, which is the solution;
Not sure where you saw a -2, need a time stamp on that one? If you are struggling with theses steps, might I suggest you start at the beginning of the course? My website is completely free:
GreeneMath.com

[@reydichos8560]

@@Greenemathahh okaay'2 THANK YOU SO MUCH!

[@Greenemath]

@@reydichos8560 You are very welcome!

[@ivmm3340]

Thanks😊👍

[@Greenemath]

You are welcome! :)

[@thefightreport69]

Brian mclogan is confusing af

[@Greenemath]

Math is a very hard subject to learn.