ENDX-290 JAV Clearly, the given expression is undefined wherever the denominator equals zero because division by zero is undefined. Therefore, to find the domain of the function, we need to determine where the denominator equals zero and exclude those values from the domain. Given expression: ( frac{x}{(x - 5)(x + 4)} ) **Step 1: Identify the denominator** The denominator is ( (x - 5)(x + 4) ). **Step 2: Set the denominator equal to zero** Since division by zero is undefined, we set the denominator equal to zero and solve for ( x ): [ (x - 5)(x + 4) = 0 ] **Step 3: Solve for ( x )** [ (x - 5) = 0 quad Rightarrow quad x = 5 ] [ (x + 4) = 0 quad Rightarrow quad x = -4 ] Therefore, the expression is undefined for ( x = 5 ) and ( x = -4 ). **Step 4: Define the domain** The domain is all real numbers except ( x = 5 ) and ( x = -4 ). In interval notation, this is: [ (-infty, -4) cup (-4, 5) cup (5, +infty) ] Thus, the final answer is ( ox{ (-infty, -4) cup (-4, 5) quad (5, +infty) } ). ### Explanation **Step 1: Identify the denominator** The denominator is ( (x - 5)(x + 4) ). **Step 2: Set the denominator equal to zero** Since division by zero is undefined, we set the denominator equal to zero and solve for ( x ): [ (x - 5)(x + 4) = 0 ] **Step 3: Solve for ( x ** [ (x - 5) = 0 quad Rightarrow quad x = 5 ] [ (x + 4) = 0 quad Rightarrow quad x = -4 ] **Step 4: Define the domain** The domain is all real numbers except ( x = 5 ) and ( x = -4 ). In interval notation, this is: [ (-infty, -4) cup (-4, 5) cup (5, +infty) ] Thus, the final answer is ( ox{ (-infty, -4) cup (-4, 5) quad (5, +infty) } ). - Free Trailer and English Subtitles srt.

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