Express x-11/x²-2x-3 + 2/x-3 as a single fraction in its simplest form

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Factor Denominator: Factor the denominator of the first fraction. The denominator x² - 2x - 3 can be factored into (x - 3)(x + 1) because (x - 3)(x + 1) = x² + x - 3x - 3 = x² - 2x - 3.Rewrite First Fraction: Rewrite the first fraction with the factored denominator. The first fraction becomes (x - 11)/((x - 3)(x + 1)).Combine Fractions: Combine the two fractions. Since the second fraction already has a denominator of (x - 3), we can combine the two fractions by writing them over a common denominator, which is (x - 3)(x + 1). The combined fraction is (x - 11 + 2(x + 1))/((x - 3)(x + 1)).Distribute and Combine: Distribute and combine like terms in the numerator. Distribute the 2 in the second term of the numerator to get 2x + 2. The numerator becomes (x - 11 + 2x + 2). Combine like terms to get (3x - 9).Write Simplified Fraction: Write the simplified fraction. The simplified fraction is (3x - 9)/((x - 3)(x + 1)).Check Numerator Factor: Check if the numerator can be factored further. The numerator 3x - 9 can be factored as 3(x - 3).Cancel Common Factors: Cancel common factors. The factor (x - 3) is common to both the numerator and the denominator, so we can cancel it out. The final simplified fraction is 3/(x + 1).

Express $x-\frac{11}{x^2-2x-3} + \frac{2}{x-3}$ as a single fraction in its simplest form

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Express $x-\frac{11}{x^2-2x-3} + \frac{2}{x-3}$ as a single fraction in its simplest form