1. ## Solving equations

...(2) = ...(2x) + 3
(x + 1) (2x - 3)

The dots don't mean anything I am trying to make it look OK?

I am asked to solve the above equation!

I think my first step is to determine the denominators, so I think;

common denominators are; 3(x+1)(2x-3)

when I expand these denominators I get;

3(x+1)(2x-3) = 2x^2 - 3x + 2x = 3(2x^2 - 3x +2x) = 6x^2 - 9x + 6x = 6x^2 - 3x

So my common denominators are 3 and 6

am I right so far?

Thanks

David

2. ## Re: Solving equations

Is the problem statement:

$\displaystyle \frac{2}{x+1}=\frac{2x+3}{2x-3}$?

3. ## Re: Solving equations

Originally Posted by Quacky
Is the problem statement:

$\displaystyle \frac{2}{x+1}=\frac{2x+3}{2x-3}$?
nearly, I wished I could present the work as you do then I would not make things difficult for people?

........2x..... + 3
......2x - 3
Sorry I hope this is clearer

David

4. ## Re: Solving equations

this forum implements a math-formatting system called "latex". to write a fraction in latex, you type:

$$\frac{expression one}{expression two}$$

so $$\frac{2x}{x^2+1}$$

produces $\displaystyle \frac{2x}{x^2 + 1}$.

read this thread, it has more (note: we don't use the "math" tags anymore, we use "tex" tags).

5. ## Re: Solving equations

Originally Posted by Deveno
this forum implements a math-formatting system called "latex". to write a fraction in latex, you type:

$\displaystyle \frac{expression one}{expression two}$

so $\displaystyle \frac{2x}{x^2+1}$

produces $\displaystyle \frac{2x}{x^2 + 1}$.

read this thread, it has more (note: we don't use the "math" tags anymore, we use "tex" tags).
I am just going to try it copying your example.

{tex}\frac{2x}{x^22+1}{tex}

6. ## Re: Solving equations

use square brackets [], not curly ones {} around the tex tags. remember you start with [ tex] and end with [/tex]. the curly brackets seperate different things for the \frac function inside the tex tags.

7. ## Re: Solving equations

Originally Posted by Deveno
use square brackets [], not curly ones {} around the tex tags. remember you start with [ tex] and end with [/tex]. the curly brackets seperate different things for the \frac function inside the tex tags.
OK here I go?

13. ## Re: Solving equations

In the future, would you mind posting some working out stages rather than jumping immediately several stages ahead? It would help us to follow your logic and check your solution.

Firstly, you have no reason to do anything with the denominator. Once you've found the common denominator, just leave it as it is. Expanding it is just wasting your energy (and potentially exam time!).

When we combine everything, we get:

$\displaystyle \frac{2x(x+1)+3(x+1)(2x-3)-2x(2x-3)}{(2x-3)(x+1)}$

This is certainly a monster, so don't try to rush it. Take it term by term. I'd suggest starting by rewriting the $\displaystyle 3(x+1)$ towards the middle as $\displaystyle (3x+3)$

Then, start chronologically from the beginning and expand, using FOIL if necessary.

14. ## Re: Solving equations

Originally Posted by David Green
I don't think I will be anywhere near right to be honest, and if I put my full working out in now I am sure it would be very confusing?

However I have ended up with;

8^2 - 7 - 2x / 2x^2 - x - 7

????????
The numerator is $\displaystyle 2x(x+1) + 3(2x-3)(x+1) - 2x(2x-3)$. Expand and collect like terms (and be aware of the rule regarding subtracting negatives in the last term)

The denominator is best left as $\displaystyle (2x-3)(x+1)$ since we'll multiply both sides by this to clear the fraction and since anything multiplied by 0 is 0 we need only look at the numerator

15. ## Re: Solving equations

Originally Posted by David Green
Just having another go at latex?

$\displaystyle /frac{2x}{x^22+1}$
This is fine except that your slash is the wrong direction in the "/frac" - it should be "\frac" and I think it should be x^2 instead of x^22

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