((x+3)/(x-5))+(5/(x-3))
Simplify
I've done this twice and got it wrong both times I have two more problems similar to this and don't want to continue until I understand how to do it.
Just like in numerical fractions, you will need a common denominator , which would be (x-5)(x-3)
so we get
( (x+3)(x-3) + 5(x-5) )/((x-5)(x-3))
= (x^2 - 9 + 5x - 25)/(x^2 -8x + 15)
= (x^2 + 5x - 34)/(x^2 - 8x + 15)
Thanks that was a great help.
To simplify the expression ((x+3)/(x-5))+(5/(x-3)), we need to find a common denominator and combine the fractions.
1. Start by factoring the denominators: (x-5) and (x-3).
2. To find the common denominator, we need to identify the factors that both denominators have in common. In this case, both denominators have the factor (x-5) and (x-3).
3. Now, multiply the numerator and denominator of the first fraction, (x+3), by (x-3) to make its denominator match the common denominator:
((x+3)*(x-3))/((x-5)*(x-3)) + 5/(x-3)
Simplifying the first fraction:
(x^2 - 9)/((x-5)*(x-3)) + 5/(x-3)
4. Now, since the denominators are the same, we can add the two fractions:
(x^2 - 9 + 5)/(x-5)(x-3)
Simplifying the numerator:
(x^2 - 4)/(x-5)(x-3)
Now, the expression ((x+3)/(x-5))+(5/(x-3)) is simplified to (x^2 - 4)/((x-5)(x-3)).
Make sure to double-check your work using these steps and the original expression.