Simplify each sum or difference. State any restrictions on the variables.

19) \(\frac{-3x}{x^2 - 9} + \frac{4}{2x - 6}\)

Simplify 4 2x-6
1.1 Pull out like factors :
2x - 6 = 2 • (x - 3)
-3x Simplify ——3 over x2 -9———— x2 - 9

Answered by Anonymous | 2024-06-10

(-3x)/(x^2 - 9) + 4/(2x-6) = (-3x)/[(x-3)(x+3)] + 4/[2(x-3)] = (-3x)/[(x-3)(x+3)] + 2/(x-3) = (-3x + 2x + 6)/[(x-3)(x+3)] = (-x+6)/[(x-3)(x+3)];

Answered by crisforp | 2024-06-10

The expression − x 2 − 9 3 x ​ + 2 x − 6 4 ​ simplifies to − ( x − 3 ) ( x + 3 ) 5 x + 6 ​ . Restrictions on the variable include x  = 3 and x  = − 3 to prevent the denominator from being zero. This ensures the expression is defined for all other values of x .
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Answered by Anonymous | 2024-12-23