Rational expression pxplain your work please .
37/k^2-k-30
and x^2-25/2
To simplify the rational expressions, we need to factor the numerator and denominator (if possible) and cancel any common factors.
1) Rational Expression: 37/(k^2 - k - 30)
To factor the denominator, we are looking for two numbers, let's call them a and b, whose product is equal to -30 and whose sum is equal to -1 (the coefficient of k in this case).
Factors of -30:
-1, 30
1, -30
-2, 15
2, -15
-3, 10
3, -10
-5, 6
5, -6
Since -5 + 6 = 1, we can rewrite the denominator as:
k^2 - 5k + 6k - 30
(k^2 - 5k) + (6k - 30)
k(k - 5) + 6(k - 5)
(k + 6)(k - 5)
Now, the rational expression becomes:
37/[(k + 6)(k - 5)]
2) Rational Expression: (x^2 - 25)/2
The numerator, x^2 - 25, can be factored using the difference of squares formula:
x^2 - 25 = (x + 5)(x - 5)
The rational expression becomes:
(x + 5)(x - 5)/2
These are the simplified forms of the given rational expressions.