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Simplify (x^2 - 25)/(x^2 + 10x + 25).

 Nov 15, 2019
 #1
avatar+470 
+3

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!

 Nov 15, 2019
 #2
avatar+58 
+2

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

 Nov 15, 2019
 #3
avatar+105370 
+2

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

 

 

 

cool cool cool

 Nov 15, 2019

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