How to Simplify a Fraction to Quadratic Form?

[alpha01]

can someone show how to simplify \frac{12x+9}{x} = x+9 so that it is in the quadratic form: x^2 -3x -9 = 0

multiplying both sides by x, subtracting both sides by 9 etc. . doesn't give me the quadratic.

 

[tiny-tim]

Hi alpha01!

erm … I think you put 9 on the right-hand side instead of 9x.

 

[mubashirmansoor]

Just multiply both sides by 'x' :

( x (12x + 9 ) ) / x = x ( x + 9 )

multiplied x on the left hand side cancels out with its denominator & by expanding the right hand side you will get;

12x + 9 = x^2 + 9x

Subtracting both sides by (12x + 9);

0 = x^2 +9x - 12x - 9

which means;

x^2 - 3x - 9 = 0

& that's what you are looking for...

 

[alpha01]

Subtracting both sides by (12x + 9);

thanks

 

[mubashirmansoor]

Your welcome ! :)

 

[ice109]

Hi alpha01!

erm … I think you put 9 on the right-hand side instead of 9x.

how would he get a quadratic then

 

[ice109]

sorry misread and now i can't delete