# Solution of a quadratic parametric equation

#### ryloth

##### New member
I am trying to solve the attached quadratic parametric equation.
I have just simplify a bit the denominator by collecting a couple of terms, but I am stuck there.
Thank you a lot.

Sorry for the low quality of the image.

Gianluca

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#### tkhunny

##### Moderator
Staff member
I am trying to solve the attached quadratic parametric equation.
I have just simplify a bit the denominator by collecting a couple of terms, but I am stuck there.
Thank you a lot.

View attachment 11006

Sorry for the low quality of the image.

Gianluca
Are you SURE it's "Quadratic"? It certainly look's quadratic in the denominators, but does that make the whole thing "quadratic"?

What do you mean by "collect"? Factoring may be a nice direction.

$$\displaystyle \dfrac{1}{(x+2k)(x-(k+1))} = \dfrac{x}{(x+2k)(x-2k)}$$

A common denominator may help you on your way.

Note: "Parametric" usually means that there is some independent variable that controls all the other variables. It doesn't normally mean that there is a arbitrary parameter included ('k' in your example). Anyway, your question was understandable.

#### ryloth

##### New member
Thank you very much.
Indeed I am not used to math terms (I am more confident with biochemistry) and vocabulary gives not much help.

In italian those kind of equations are defined as 'equazioni di secondo ordine parametriche'.

I was eventually able to solve it.

Gianluca

#### Subhotosh Khan

##### Super Moderator
Staff member
I am trying to solve the attached quadratic parametric equation.
I have just simplify a bit the denominator by collecting a couple of terms, but I am stuck there.
Thank you a lot.

View attachment 11006

Sorry for the low quality of the image.

Gianluca
$$\displaystyle \displaystyle{\dfrac{1}{x^2 + (k-1)x - 2k^2 - 2k} = \dfrac{x}{x^2 - 4k^2}}$$

Last edited:

#### tkhunny

##### Moderator
Staff member
Thank you very much.
Indeed I am not used to math terms (I am more confident with biochemistry) and vocabulary gives not much help.

In italian those kind of equations are defined as 'equazioni di secondo ordine parametriche'.

I was eventually able to solve it.

Gianluca
Fair enough. Thanks for sharing the translation.