# How do you simplify the expression #(x+6)/(x^2-4) - (x-3)/(x+2) + (x-3)/(x-2)#?

Taking the LCM

Expand

Collect like terms

Simplify

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To simplify the expression (x+6)/(x^2-4) - (x-3)/(x+2) + (x-3)/(x-2), we need to find a common denominator for all the fractions. The common denominator is (x^2-4)(x+2)(x-2).

Next, we multiply each fraction by the appropriate factor to obtain the common denominator.

For the first fraction (x+6)/(x^2-4), we multiply the numerator and denominator by (x+2)(x-2).

For the second fraction (x-3)/(x+2), we multiply the numerator and denominator by (x^2-4).

For the third fraction (x-3)/(x-2), we multiply the numerator and denominator by (x+2).

After multiplying, we can combine the numerators over the common denominator.

The simplified expression is (x^2 - 3x + 6)/(x^3 - 4x^2 - 4x + 16).

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