Question

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Using complete sentences, describe how you would check the quotient of two rational expressions. Create and demonstrate your own example of this concept.

Answer 1

To check the quotient of a division problem, I would multiply the quotient by the divisor and add the remainder. If the quotient is correct, the result will be the dividend.
\[\frac{ x ^{2}-x-6 }{ x-3 }\] = \[\frac{ (x-3) (x+2) }{ x-3 }\]=x+2
To check this, I will multiply the quotient which is x+2 by the divisor which is x-3. It the result is correct, I with get
\[x ^{2}-x-6\]
\[(x+2)(x-3)=x ^{2}-3x+2x-6=x ^{2}-x-6\]