Question #10b08
1 Answer
Your answer is incorrect. A correct simplification could include
Explanation:
As with most fractions, we should try to find a common denominator.
The first fraction's denominator can be factored as a difference of squares:
#x^2/(x^2-4)-(x+1)/(x-2)=x^2/((x+2)(x-2))-(x+1)/(x-2)#
We now should see that the least common denominator is
#x^2/((x+2)(x-2))-(x+1)/(x-2)=x^2/((x+2)(x-2))-((x+1)(x+2))/((x+2)(x-2))#
Simplify the numerator of the second fraction by FOILing
#x^2/((x+2)(x-2))-((x+1)(x+2))/((x+2)(x-2))=x^2/((x+2)(x-2))-(x^2+3x+2)/((x+2)(x-2))#
Since the fractions have the same denominator, we can combine the numerators. Be careful, though--since the second fraction is being subtracted, we will have to use parentheses and subtract the entire numerator of the second denominator:
#x^2/((x+2)(x-2))-(x^2+3x+2)/((x+2)(x-2))=(x^2-(x^2+3x+2))/((x+2)(x-2))#
Distributing the negative:
#(x^2-(x^2+2x+3))/((x+2)(x-2))=(x^2-x^2-3x-2)/((x+2)(x-2))#
Canceling:
#(x^2-x^2-3x-2)/((x+2)(x-2))=(-3x-2)/((x+2)(x-2))#
This could also be written as any of the following:
#(-3x-2)/((x+2)(x-2))=-(3x+2)/((x+2)(x-2))=-(3x+2)/(x^2-4)=(3x+2)/(4-x^2)#