MHB Practice problems of Rational Equations ?

[kupid]

Does anyone know where i can find some practice problems of Rational Equations ?

 

[skeeter]

https://www.google.com/search?safe=....hp..0.19.252...46j0i131k1j0i46k1.Gf2L704nKDg

 

[kupid]

I don't know how to take the LCM of the denominators when the denominators are algebraic terms .

For example ,

View attachment 6704

How do i take the LCM there ? Do we simply multiply the terms in the denominator ?

 

[I like Serena]

I don't know how to take the LCM of the denominators when the denominators are algebraic terms .

For example ,
How do i take the LCM there ? Do we simply multiply the terms in the denominator ?

Hi kupid,

The least common denominator (LCD) of a set of fractions is the least number that is a multiple of all the denominators.
In this case that means indeed that we simply multiply the denominators.
That only changes if the denominators have a factor in common.

 

[kupid]

Thanks

But i don't know how to check for common factors when the denominators are algebraic terms .

How do we check for common factors when the denominators are algebraic terms ?

 

[I like Serena]

Thanks

But i don't know how to check for common factors when the denominators are algebraic terms .

How do we check for common factors when the denominators are algebraic terms ?

By factoring denominators to the form (x-a)(x-b)(x-c).
If both denominators contain (x-a), then the LCD has (x-a) only once.

 

[kupid]

Oh , That is how you find the LCM in such cases ? Thanks a lot :-)

 

[skeeter]

using the example you posted earlier ...

$\dfrac{4}{x+2} + 3 = \dfrac{3x}{x-3}$

$\dfrac{4\color{red}{(x-3)}}{(x+2)\color{red}{(x-3)}} + \dfrac{3\color{red}{(x+2)(x-3)}}{\color{red}{(x+2)(x-3)}}= \dfrac{3x\color{red}{(x+2)}}{(x-3)\color{red}{(x+2)}}$

$4(x-3) + 3(x+2)(x-3) = 3x(x+2)$ ; $x \ne \{-2,3\}$

 

[kupid]

Thanks ,

I was going through this book .

https://2012books.lardbucket.org/books/beginning-algebra/s10-rational-expressions-and-equat.html

I think i found a nice definition

It is not always the case that the LCD is the product of the given denominators. Typically, the denominators are not relatively prime; thus determining the LCD requires some thought. Begin by factoring all denominators.
The LCD is the product of all factors , with the highest power

 

[skeeter]

bottom line (no pun intended) ... just make all the denominators the same using the least number of common factors possible

 

[kupid]

Thanks ,To calculate an LCM for a rational function, follow these steps:
1. Factor all denominator polynomials completely.
2. Make a list that contains one copy of each factor, all multiplied together.
3. The power of each factor in that list should be the highest power that factor is
raised to in any denominator.
4. The list of factors and powers you generated is the LCM.