Simplify Fractions: (3-x)(x+2)(2x+9) < 0 | Multiply and Solve

Thread starter MrNeWBiE
Start date Mar 15, 2010
Tags

Fractions

AI Thread Summary

The discussion centers on simplifying the inequality 2x+9/(3-x)(x+2) < 0 by multiplying both sides by (3-x)(x+2), resulting in (3-x)(x+2)(2x+9) < 0. Participants clarify that multiplying by (3-x)^2(x+2)^2 maintains the inequality's direction since these factors are always positive. The conversation emphasizes the importance of ensuring that the multiplication does not affect the inequality's validity. Overall, the focus is on understanding how to manipulate the inequality correctly while maintaining its properties. The participants express enthusiasm and support for each other's learning process.

Mar 15, 2010

MrNeWBiE

question in fractions,,,

how

2x+9/(3-x)(x+2) < 0

became

(3-x)(x+2)(2x+9) < 0 " multiply both sides "

zero is in the other side ,,,

Physics news on Phys.org

Mar 15, 2010

tiny-tim

Science Advisor

Homework Helper

Hi MrNeWBiE!

'cos one is (3-x)²(x+2)² times the other … which is always positive!

Mar 15, 2010

MrNeWBiE

so i multiply both sides with ====> (3-x)^2(x+2)^2

Mar 15, 2010

tiny-tim

Science Advisor

Homework Helper

(try using the X² tag just above the Reply box

)

Yup!

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

View full post »