Fully factorise and simplify (x^2 +7x + 10) / (x^2 - 25)

Simplify the numerator (top) by finding the pair of numbers which multiply together to give the C term of the quadratic, and add to give the B term. This gives 2 and 5 so the equation becomes (x+2)(x+5) / (x^2 - 25)Using the difference of two squares, the denominator can be split into (x+5)(x-5)The equation is now (x+2)(x+5) / (x+5)(x-5) and we can cancel out the (x+5) terms from the top and bottom, giving us a final answer of (x+2) / (x-5)