Solving an equations with rational expressions

👉 Learn how to solve rational equations. A rational expression is an expression in the form of a fraction where the numerator and/or the denominator are/is an algebraic expression. There are many ways to solve rational expressions, one of the ways is by multiplying all the individual rational expressions by the lowest common multiply (LCM) of the denominators. This eliminates the denominators and then we can evaluate the resulting equation accordingly.

It is very helpful to check your results by substituting them into the original equation to see if they are true. This also helps to identify the extraneous solutions. An extraneous solution is a solution that is obtained during the course of solving an equation but which does not hold true for the original equation.

Organized Videos:
✅ How to Solve Rational Equations
✅ How to Solve Rational Equations with Trinomials
✅ How to Solve Rational Equations with Binomials
✅ How to Solve Rational Equations with Monomials
✅ How to Solve Rational Equations with an Integer
✅ How to Solve Rational Equations | Learn About
✅ How to Solve Proportions with Binomials
✅ How to Solve Proportions with Trinomials

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[marcasu]

Youre a blessing to the entire world!! Thanks so much for your work

[ChavoMysterio]

I would have subtracted 5/6 from both sides to turn it into a proportional equation, then cross multiplied.
[4/(x+3)]-5/6 = 23/18
[4/(x+3)] = 8/18 add 5/6 to both sides
[4/(x+3)] = 4/9 simplify fraction on right side
4(x+3) = 36 cross multiply
x+3 = 9 divide both sides by 4
x = 6 subtract 3 from both sides

[irwandasaputra]

4:(x+3)=23/18-5/6
4:(x+3)=23/18-15/18
4:(x+3)=8/18
4:(x+3)=4/9
36=4x+12
9=x+3
x=9-3
x=6

[RamSharma-zpfx]

Hey Brian. I'm really confused here.
Please help me out if possible.


I think it's safe to say that the required technique while simplifying rational expressions closely mirrors that of the techniques used in simplifying basic fractions.


While computing basic fractions in the event of unlike denominators, the LCD is ascertained.
Then next step here, as far as I can tell, is to observe the denominator and to then multiply the numerator with the number which was needed for the denominator to satisfy the newfound lcd.


For instance, if I have a fraction alongside other fractions, let's say, [3/6], and my ascertained LCD is 12, I would multiply 3 (the numerator) with 2, because that is what is needed for my denominator to satisfy the newfound LCD.





But here, in the case of rational expressions, which should otherwise mirror the above basic process, seems to bypass this convention.


Instead of multiplying the numerator with the number needed to satisfy the lcd in terms of the denominator, you simply multiply the numerator with the lcd. Why?


In basic fractions, one surely can't just multiply the numerator with the LCD.. I don't believe it works that way?
Clearly, I'm missing something. Help.