1. ## Simple algebra problem

Hello,

I am new to algebra and would really appreciate some analysis of the logic of the following equation. I am working through a textbook on fundamentals of mathematics and we start with the original equation:

$\displaystyle \frac{\sqrt{3x^2+x}}{2\sqrt{x}}=7$

To remove the square root and simplify the equation we square each side of the equation and the resulting formula is:

$\displaystyle \frac{3x^2+x}{4x}=49$

Upto that part I am fine. Next, the text book says that we should cancel x in the numerator and denominator on the left hand side only. I understand why we are only doing it on the left hand side - i.e. we are cancelling down to the simplest expression. However, I don't quite understand how we end up with the following equation after cancelling out i.e.:

$\displaystyle \frac{(3x+1)}{4}=49$

Kind Regards,
Raheel

2. Originally Posted by hennanra
Hello,

I am new to algebra and would really appreciate some analysis of the logic of the following equation. I am working through a textbook on fundamentals of mathematics and we start with the original equation:

$\displaystyle \frac{\sqrt{3x^2+x}}{2\sqrt{x}}=7$

To remove the square root and simplify the equation we square each side of the equation and the resulting formula is:

$\displaystyle \frac{3x^2+x}{4x}=49$

Upto that part I am fine. Next, the text book says that we should cancel x in the numerator and denominator on the left hand side only. I understand why we are only doing it on the left hand side - i.e. we are cancelling down to the simplest expression. However, I don't quite understand how we end up with the following equation after cancelling out i.e.:

$\displaystyle \frac{(3x+1)}{4}=49$

Kind Regards,
Raheel

$\displaystyle \frac{(3x+1)}{4} \times 4 =49 \times 4$

$\displaystyle 3x+1 = 196$

$\displaystyle 3x = 195$

$\displaystyle x = 65$

3. Many thanks for the reply. Actually, the equation is also solved in the book and the book is using simplistic (sometimes long winded) methods in areas to demonstrate certain principles. My question is mainly related to the actual cancelling out.

I can see that your method is far more effective, it was more a case of trying to understand that part of the equation that I mentioned - i.e. how does it end up in the form described - i.e. how exactly does the cancelling out achieve the change in the formula that I have stated.

Kind Regds,
Raheel

4. Originally Posted by hennanra
Many thanks for the reply. Actually, the equation is also solved in the book and the book is using simplistic (sometimes long winded) methods in areas to demonstrate certain principles. My question is mainly related to the actual cancelling out.

I can see that your method is far more effective, it was more a case of trying to understand that part of the equation that I mentioned - i.e. how does it end up in the form described - i.e. how exactly does the cancelling out achieve the change in the formula that I have stated.

Kind Regds,
Raheel
Oh sorry, i see what you mean.

Do you agree that:

$\displaystyle \frac{3x^2+x}{4x} = \frac{x(3x+1)}{x(4)}$

Then cancel out $\displaystyle x$

5. Thank you very much.

6. Originally Posted by hennanra
Thank you very much.
You're welcome