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(x^(2)-7x-8)/(x^(2)-64)

x2−7x−8x2−64 \frac{x^{2}-7 x-8}{x^{2}-64}

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Full solution

Q. x2−7x−8x2−64 \frac{x^{2}-7 x-8}{x^{2}-64}
  1. Factor Numerator and Denominator: Factor the numerator and the denominator.\newlineThe numerator x2−7x−8x^2 - 7x - 8 can be factored into (x−8)(x+1)(x - 8)(x + 1) because (x−8)(x+1)=x2+x−8x−8=x2−7x−8(x - 8)(x + 1) = x^2 + x - 8x - 8 = x^2 - 7x - 8.\newlineThe denominator x2−64x^2 - 64 is a difference of squares and can be factored into (x−8)(x+8)(x - 8)(x + 8) because (x−8)(x+8)=x2−64(x - 8)(x + 8) = x^2 - 64.
  2. Cancel Common Factors: Cancel out the common factors.\newlineThe common factor in the numerator and the denominator is (x−8)(x - 8).\newlineSo, (x−8)(x+1)/(x−8)(x+8)(x - 8)(x + 1) / (x - 8)(x + 8) simplifies to (x+1)/(x+8)(x + 1) / (x + 8) after canceling out the (x−8)(x - 8) term.
  3. Write Simplified Expression: Write the simplified expression.\newlineThe simplified form of the expression is (x+1)/(x+8)(x + 1) / (x + 8).

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