Is the problem statement:
?
...(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
this forum implements a math-formatting system called "latex". to write a fraction in latex, you type:
[tex]\frac{expression one}{expression two}[/tex]
so [tex]\frac{2x}{x^2+1}[/tex]
produces .
read this thread, it has more (note: we don't use the "math" tags anymore, we use "tex" tags).
[Tex]\frac{2x}{x^2+1}[\tex] But use / instead of \
Anyway, so we have:
I think.
There are a few ways that you could go about this. I'd start by collecting everything on one side of the equation:
Now, you could, if you wanted to, find a common denominator. The lowest common denominator isn't actually affected by the though because we can manipulate this to match anything we want. Just look at the algebraic fractions. is the lowest common denominator for both of them. So I multiply both the numerator and denominator by the missing components, as it were, one at a time.
Hopefully you should be able to see that the parts in red cancel to give us exactly what we had in the stage above. I've multiplied through both the numerator and denominator by the same value, so I haven't changed anything - the denominators are now exactly the same. Can you combine and expand them? You need to rewrite everything as one fraction. You don't need to change the denominators at all.
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:
This is certainly a monster, so don't try to rush it. Take it term by term. I'd suggest starting by rewriting the towards the middle as
Then, start chronologically from the beginning and expand, using FOIL if necessary.
The numerator is . Expand and collect like terms (and be aware of the rule regarding subtracting negatives in the last term)
The denominator is best left as 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