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To simplify polynomial fractions, you can factor and find canceling x-intercepts.

$x^2-25 \over x^2+10x + 25$can be factored in both the numerator and denominator. $x^2 -25$ becomes $(x+5)(x-5)$, and 

$x^2+10x+25$ becomes $(x+5)(x+5)$.

From there you can get $(x+5)(x-5) \over (x+5)(x+5)$.

You can then eliminate one $x+5$ from each part of the fraction, resulting in $x-5 \over x+5$.

If no obvious factors are there, you can always use the quadratic formula to find them when the highest power is 2.

Hope this helps!

Guest, here are some easy identities for simplifying quadratics.

First, if a quadratic is in the form a^2 - b^2, then the form of the factored equation would be (a+b)(a-b). This is called the difference of squares.

Second, if in the normal quadratic form of ax ^2 + bx + c, then one must find a number that adds up to b, and multiplies to c. If a is a coefficient of a > 1, then one must find a number that adds to b and multiplies to ac. 
 

Hope this helps!

BasicMaths

THX, ZZZZZZ and BasicMaths.....!!!!!!