+476 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!
+108 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
