You can put this solution on YOUR website!
.
Because you didn't use parentheses, the rules of math say that your problem should be interpreted
as above.
.
In simplifying that problem, note that the +5 and the -5 cancel each other. Then the two terms
. and can be added to and these to operations reduce your problem
to:
.
.
This can be further simplified by getting the two terms to have a common denominator of
x. Do this by multiplying the x by which is equivalent to multiplying the x by 1
since is equivalent to 1
.
The expression is then:
.
.
and that's the simplification of the expression the way you wrote it. If you had used
parentheses to lump things together, I think you meant to write:
.
(x+5)/(x-5) - (3/(x+5))
.
And that would translate to:
.
.
And as you can see, that's a whole different problem. Parentheses are very important if you
are trying to communicate what you really mean.
.
To solve this problem, we again need to get a common denominator. That denominator is
(x-5)*(x+5).
.
To get the first term over the common denominator multiply it by .
This multiplication is:
.
.
And if you square the numerator it becomes :
.
.
That takes care of the first part of the problem. The second part consists of placing the second
term over the common denominator also. Recall that the second term was:
.
.
Put it over the common denominator by multiplying it by . This multiplication
results in:
.
.
Now we can get the total answer because the two terms are over a common denominator.
Because of that we can add the numerators of the two terms and place the sum over the
common denominator. The first term plus the second term is:
.
.
The numerator of the combination becomes:
.
.
And this simplifies to . Putting this over the common denominator
makes the answer:
.
.
And if you multiply out the common denominator, the result is:
.
.
I hope this impresses you with the difference in the two interpretations of the problem you
presented. The use of parentheses make these two answers completely different and shows
why it's so important to group terms to say what you really mean.
.
(