Q. Simplify. Write your answer using whole numbers and variables.7r−87r2−8r
Identify Terms: Identify like terms and simplify the numerator and denominator separately.The 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 7r2 and −8r are not like terms), and the denominator is already simplified (7r and −8 are not like terms).
Factor Out GCF: Factor out the greatest common factor in the numerator.The greatest common factor in the numerator that r has is r itself. We can factor r out of the numerator.7r2−8r=r(7r−8)
Cancel Common Factors: Simplify the fraction by canceling out common factors.We now have the fraction (r(7r−8))/(7r−8). We can see that the binomial (7r−8) is common to both the numerator and the denominator. However, we cannot cancel out (7r−8) from the numerator and denominator because r is also a factor in the numerator. We can only cancel out factors that are common to both the numerator and the denominator. Since r is not a factor in the denominator, we cannot cancel out the binomial (7r−8).
Check Further Simplification: Check for any further simplification.Since we cannot cancel out the binomial (7r−8), the expression is already in its simplest form. There is no further simplification possible.
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