Find the difference 7/x^2-7x - 5/x^2-49

Rewriting the expression we have:

(7 / (x ^ 2-7x)) - (5 / (x ^ 2-49))

Rewriting the denominator:

(7 / (x * (x-7))) - (5 / ((x-7) (x + 7)))

(1 / (x-7)) * ((7 / x) - (5 / (x + 7)))

Rewriting we have:

(1 / (x-7)) * (((7x + 49) + (-5x)) / (x * (x + 7)))

(1 / (x-7)) * ((2x + 49) / (x * (x + 7)))

((2x + 49) / (x * (x + 7) * (x-7)))

Answer:

The difference is:

((2x + 49) / (x * (x + 7) * (x-7)))