(x+1)/(x+3)(x-3) + 4(x-3)/(x-3)(x+3) + (x-1)(x-3)/ (3-x)(x+3) please explain how you get it
Since that is not an equation, and I have no idea what problem it is supposed to be the solution of, I cannot explain how you or anyone "got" it.
If you post this again in more complete form, please use brackets to clarify what the denominators are.
ok the question is [(x+1) divided by (x+3)(x-3)] plus [4(x-3) divided by (x-3)(x+3)] plus [(x-1)(x-3) divided by (3-x)(x+3)] i am not really sure how else to explain it. it is adding rational expression with 3 different fractions all added together. i need to get a common denominator. please if possible show me how you get the answer.. sorry if you cant understand it
Did you notice that your denominators are "almost" the same already??
If the factor in the last fraction had been (x-3) instead of (3-x) you would be all set.
Well, why don't we make the last term from
..+ (x-1)(x-3)/[(3-x)(x+3)] to
..- (x-1)(x-3)/[(x-3)(x+3)]
(notice I multiplied top and bottom by -1)
now just expand your numerators, collect all like terms and you are done.
wouldnt that make the bottom one be (x-3)(x-3) since you would have to multiply both of the bottom terms by -1
no
if you multiply both, then you are in effect multiplying by (-1) by (-1), which would produce no change at all
eg. if you multiply (3)(4) by -1 would you multiply both??
To simplify the expression:
Step 1: Start by finding the common denominator for all three fractions, which is (x+3)(x-3).
Step 2: Rewrite each fraction with the common denominator:
For the first fraction, we already have the common denominator, so no changes are needed.
For the second fraction, we can see that (x-3)/(x-3) will simplify to 1, so we have 4(x-3)/(x+3).
For the third fraction, we can simplify (3-x) to -(x-3), so we have -(x-1)(x-3)/(x+3).
Step 3: Now that we have a common denominator for all three fractions, we can combine them into a single fraction:
[(x+1) + 4(x-3) - (x-1)(x-3)] / [(x+3)(x-3)]
Step 4: Simplify the expression within the numerator:
Starting with [(x+1) + 4(x-3) - (x-1)(x-3)], we distribute the 4 to get [(x+1) + 4x - 12 - (x-1)(x-3)].
Next, expand the product of (x-1)(x-3) using FOIL method: (x-1)(x-3) = x^2 - x - 3x + 3 = x^2 - 4x + 3.
So our expression becomes [(x+1) + 4x - 12 - (x^2 - 4x + 3)].
Simplifying further, we combine like terms: x + 1 + 4x - 12 - x^2 + 4x - 3.
This simplifies to: -x^2 + 9x - 14.
Step 5: Rewrite the simplified expression:
Now, we have -x^2 + 9x - 14 as the numerator and the common denominator (x+3)(x-3).
So, the final expression is: (-x^2 + 9x - 14) / [(x+3)(x-3)].
This is the simplified form of the given expression.