x^2+5X/(x^3-25x)(x-5)^-1
To simplify the expression (x^2+5x)/(x^3-25x)(x-5)^-1, we need to apply some basic algebraic simplification rules.
First, let's simplify the denominator. We can do this by factoring x^3 - 25x using the difference of cubes formula.
x^3 - 25x = (x)^3 - (5)^2(x) = (x - 5)(x^2 + 5x + 25)
Now our expression becomes:
(x^2 + 5x)/((x - 5)(x^2 + 5x + 25))(x - 5)^-1
Next, we can simplify the denominator further by multiplying (x - 5) and (x - 5)^-1. When we multiply a number and its reciprocal, we get 1. Therefore, (x - 5)(x - 5)^-1 simplifies to 1.
Now our expression becomes:
(x^2 + 5x)/(x^2 + 5x + 25)
Finally, notice that x^2 + 5x appears in both the numerator and the denominator. We can cancel them out, leaving us with:
1/(x^2 + 5x + 25)
So, the simplified expression is 1/(x^2 + 5x + 25).