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Simplify. Write your answer using whole numbers and variables.\newline7r28r7r8\frac{7r^2 - 8r}{7r - 8}

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Q. Simplify. Write your answer using whole numbers and variables.\newline7r28r7r8\frac{7r^2 - 8r}{7r - 8}
  1. Identify Terms: Identify like terms and simplify the numerator and denominator separately.\newlineThe expression is a fraction with a polynomial in the numerator and a binomial in the denominator. We need to look for like terms to combine in the numerator and the denominator. However, in this case, there are no like terms to combine in the numerator 7r27r^2 and 8r-8r are not like terms), and the denominator is already simplified (7r7r and 8-8 are not like terms).
  2. Factor Out GCF: Factor out the greatest common factor in the numerator.\newlineThe greatest common factor in the numerator that rr has is rr itself. We can factor rr out of the numerator.\newline7r28r=r(7r8)7r^2 - 8r = r(7r - 8)
  3. Cancel Common Factors: Simplify the fraction by canceling out common factors.\newlineWe now have the fraction (r(7r8))/(7r8)(r(7r - 8))/(7r - 8). We can see that the binomial (7r8)(7r - 8) is common to both the numerator and the denominator. However, we cannot cancel out (7r8)(7r - 8) from the numerator and denominator because rr is also a factor in the numerator. We can only cancel out factors that are common to both the numerator and the denominator. Since rr is not a factor in the denominator, we cannot cancel out the binomial (7r8)(7r - 8).
  4. Check Further Simplification: Check for any further simplification.\newlineSince we cannot cancel out the binomial (7r8)(7r - 8), the expression is already in its simplest form. There is no further simplification possible.

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