How to Simplify a Fraction to Quadratic Form?

In summary, to simplify the equation \frac{12x+9}{x} = x+9 into the quadratic form x^2 -3x -9 = 0, you can multiply both sides by x and expand the right-hand side. This will result in the equation x^2 - 3x - 9 = 0, which is in the desired quadratic form. Make sure to subtract both sides by (12x + 9) to get the final answer.
  • #1
alpha01
77
0
can someone show how to simplify [tex]\frac{12x+9}{x} = x+9[/tex] 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.
 
Mathematics news on Phys.org
  • #2
Hi alpha01! :smile:

erm … I think you put 9 on the right-hand side instead of 9x. :redface:
 
  • #3
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...
 
  • #4
mubashirmansoor said:
Subtracting both sides by (12x + 9);
thanks
 
  • #5
Your welcome ! :)
 
  • #6
tiny-tim said:
Hi alpha01! :smile:

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

how would he get a quadratic then :confused:
 
  • #7
sorry misread and now i can't delete
 

1. What is "simplify to quadratic form"?

"Simplify to quadratic form" is a mathematical process used to transform an expression with higher degree terms into a quadratic expression. This can make solving the expression easier and more efficient.

2. When is it necessary to simplify to quadratic form?

Simplifying to quadratic form is necessary when working with expressions that have terms with degrees higher than two, such as cubic or quartic expressions. This process allows for easier manipulation and solving of the expression.

3. How do you simplify to quadratic form?

To simplify to quadratic form, you need to use algebraic techniques to rearrange the expression into the form ax^2 + bx + c, where a, b, and c are constants. This may involve factoring, completing the square, or using the quadratic formula.

4. Why is it important to simplify to quadratic form?

Simplifying to quadratic form can make solving an expression easier and more efficient. It also allows for easier identification of key components, such as the vertex, axis of symmetry, and solutions of the expression.

5. Can simplifying to quadratic form be applied to any expression?

No, simplifying to quadratic form is only applicable to expressions with terms of degree higher than two. Expressions with only linear or quadratic terms do not need to be simplified to quadratic form.

Similar threads

  • General Math
Replies
16
Views
3K
Replies
7
Views
821
  • General Math
Replies
5
Views
939
Replies
11
Views
987
Replies
7
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
905
  • General Math
Replies
1
Views
680
Replies
5
Views
1K
Replies
5
Views
706
Back
Top