simplify the following rational expression: 4(x+2)^8 (x-3)^6
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20(x+2)^2 (x-3)^12
note:the expression is all together.sorry for how it looks.
4/20 = 1/5
a^8/a^2 = a^6
b^6/b^12 = b^-6 or 1/b^6
so
(1/5)[(x+2)/(x-3)]^6
To simplify the given rational expression, we can cancel out common factors in the numerator and denominator.
Let's start by factoring out common factors:
Numerator: 4(x+2)^8 (x-3)^6
Denominator: 20(x+2)^2 (x-3)^12
Now, let's cancel out the common factors:
Numerator: 4 * (x+2)^8 * (x-3)^6
Denominator: 4 * 5 * (x+2)^2 * (x-3)^12
After canceling out the common factors, we are left with:
Numerator: (x+2)^8 * (x-3)^6
Denominator: 5 * (x+2)^2 * (x-3)^12
The final simplified expression is:
(x+2)^8 * (x-3)^6
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5 * (x+2)^2 * (x-3)^12