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x+8x2−6x−7   x2+16x+64x+1   \dfrac{\dfrac{x+8}{x^2-6x-7}}{\,\,\,\dfrac{x^2+16x+64}{x+1}\,\,\,}

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Evaluate definite integrals using the chain ruleright chevron icon

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Q. x+8x2−6x−7   x2+16x+64x+1   \dfrac{\dfrac{x+8}{x^2-6x-7}}{\,\,\,\dfrac{x^2+16x+64}{x+1}\,\,\,}
  1. Factorize: Factorize the denominators and numerators where possible.\newlinex+8x2−6x−7\dfrac{x+8}{x^2-6x-7} can be rewritten as x+8(x−7)(x+1)\dfrac{x+8}{(x-7)(x+1)}.\newlinex2+16x+64x+1\dfrac{x^2+16x+64}{x+1} can be rewritten as (x+8)2x+1\dfrac{(x+8)^2}{x+1}.
  2. Rewrite fraction: Rewrite the complex fraction using the factorizations.\newlinex+8(x−7)(x+1)(x+8)2x+1\dfrac{\dfrac{x+8}{(x-7)(x+1)}}{\dfrac{(x+8)^2}{x+1}}.
  3. Apply property: Apply the property of division of fractions, which is multiplying by the reciprocal.\newlinex+8(x−7)(x+1)⋅x+1(x+8)2\dfrac{x+8}{(x-7)(x+1)} \cdot \dfrac{x+1}{(x+8)^2}.
  4. Simplify terms: Simplify by canceling out common terms.\newlineThe x+1x+1 and one x+8x+8 cancel out, leaving 1x−7⋅1x+8\dfrac{1}{x-7} \cdot \dfrac{1}{x+8}.
  5. Multiply fractions: Multiply the remaining fractions.\newline1(x−7)(x+8)\dfrac{1}{(x-7)(x+8)}.

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