Can someone show me how to find the sum of this equation and put it in it's simpliest form?
(x^2)/(x^2-25)+(7x+10)/(x^2-25)
They have a common denominator:
x^2-25 which can factor to (x+5)(x-5)
The numerator will add to
x^2+7x +10 which can factor to
(x+5)(x+2)
Notice the numerator and denominator have a common factor which will divid out.
To find the sum of the given equation and put it in its simplest form, you first need to find a common denominator for the two fractions. In this case, the common denominator is (x^2 - 25), which can be factored as (x + 5)(x - 5).
Next, you'll need to simplify the numerators. The first numerator (x^2) cannot be simplified further, while the second numerator (7x + 10) can be factored as (x + 5)(x + 2).
Now that you have the common denominator and simplified numerators, you can rewrite the equation as follows:
(x^2)/(x^2 - 25) + (7x + 10)/(x^2 - 25)
= (x^2)/[(x + 5)(x - 5)] + (7x + 10)/[(x + 5)(x - 5)]
Since the fractions have a common denominator, you can now add the numerators over the common denominator:
= [(x^2) + (7x + 10)]/[(x + 5)(x - 5)]
= [x^2 + 7x + 10]/[(x + 5)(x - 5)]
Finally, the numerator can be factored as (x + 2)(x + 5). Therefore, the simplified form of the equation is:
= [(x + 2)(x + 5)]/[(x + 5)(x - 5)]
= (x + 2)/(x - 5)
So, the sum of the given equation in its simplest form is (x + 2)/(x - 5).