Q. Simplify. Write your answer using whole numbers and variables.r2−rr−1
Identify Terms and Operation: Identify the terms and the operation to be performed. We have an expression with a variable r, and we need to simplify it by performing the subtraction and division operations.
Factor Denominator: Factor the denominator of the fraction.The denominator r2−r can be factored by taking out the common factor r.r2−r=r(r−1)
Rewrite with Factored Denominator: Rewrite the expression with the factored denominator.The expression becomes r−r(r−1)1.
Identify Common Denominator: Identify the common denominator to combine the terms.The common denominator for the terms is r(r−1).
Rewrite First Term as Fraction: Rewrite the first term r as a fraction over the common denominator.r can be written as 1r, and to have the common denominator, we multiply both the numerator and the denominator by r(r−1).r=r(r−1)r×r(r−1)=r(r−1)r2(r−1)
Combine Terms Over Common Denominator: Combine the terms over the common denominator.Now we have r2(r−1)/(r(r−1))−1/(r(r−1)).We can combine these over the common denominator:(r2(r−1)−1)/(r(r−1))
Distribute r2 in Numerator: Distribute the r2 across the (r−1) in the numerator.r2(r−1)=r3−r2Now the expression is (r3−r2−1)/(r(r−1)).
Simplify Expression: Simplify the expression if possible.The expression (r3−r2−1)/(r(r−1)) is already simplified as there are no common factors that can be canceled between the numerator and the denominator.
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