Algebraic equation with fractions

**tofuwrice** · September 11th 2010, 07:33 PM

Hi, I need help with this equation!

$\frac {9} {x-10} - \frac {210}{x^2 -100} = 1$

I have tried to cross multiply and factor the question and end up with

$x(-9x^2-9x+1200) = 0$

If that is in the ballpark can you help me factor that or am I completely wrong?

The book asks for

Solutions are x1= and x2= . Important Note: x1 denotes the smaller solution.

**Prove It** · September 11th 2010, 08:47 PM

Sorry but this is unreadable. Please use brackets where they're needed or learn some basic LaTeX. There is an entire subforum here dedicated to learning to use LaTeX.

**tofuwrice** · September 11th 2010, 08:53 PM

Huzzah, I have fixed my original post. Sorry for the inconvenience.

**Prove It** · September 11th 2010, 09:02 PM

Originally Posted by tofuwrice

Hi, I need help with this equation!

$\frac {9} {x-10} - \frac {210}{x^2 -100} = 1$

I have tried to cross multiply and factor the question and end up with

$x(-9x^2-9x+1200) = 0$

If that is in the ballpark can you help me factor that or am I completely wrong?

The book asks for

Solutions are x1= and x2= . Important Note: x1 denotes the smaller solution.

Cross multiplying is a method that is "in the ballpark", but the easier way is to get a common denominator.

Note that $x^2 - 100 = (x - 10)(x + 10)$ .

So $\frac{9}{x - 10} - \frac{210}{x^2 - 100} = 1$

$\frac{9(x + 10)}{(x - 10)(x + 10)} - \frac{210}{(x - 10)(x + 10)} = 1$

$\frac{9(x + 10) - 210}{(x - 10)(x + 10)} = 1$

$\frac{9x + 90 - 210}{x^2 - 100} = 1$

$\frac{9x - 120}{x^2 - 100} = 1$

$9x - 120 = 1(x^2 - 100)$

$9x - 120 = x^2 - 100$

$0 = x^2 - 9x + 20$

$0 = (x - 4)(x - 5)$

$x - 4 = 0$ or $x - 5 = 0$

$x = 4$ or $x = 5$ .

**tofuwrice** · September 11th 2010, 09:04 PM

omg, i am literally smacking my head. I can't believe i didn't see this simple solution. Thanks a lot!

Thread: Algebraic equation with fractions

LinkBack

Thread Tools

Display

Algebraic equation with fractions

Similar Math Help Forum Discussions

Algebraic Fractions

Algebraic Fractions

Algebraic Fractions

Algebraic fractions FML

[SOLVED] Partial Fractions/algebraic fractions

Search Tags