91Ó°ÊÓ

Explain how to solve a rational equation.

Explain how to find restrictions on the variable in a rational equation.

Why should restrictions on the variable in a rational equation be listed before you begin solving the equation?

Perform the indicated operation or operations. Simplify the result, if possible. $$\frac{3}{x^{2}+4 x y+3 y^{2}}-\frac{5}{x^{2}-2 x y-3 y^{2}}+\frac{2}{x^{2}-9 y^{2}}$$

Two formulas that approximate the dosage of a drug prescribed for children are $$ \begin{aligned} \text { Young's rule: } & C=\frac{D A}{A+12} \\ \text { and Cowling's rule: } & C=\frac{D(A+1)}{24} \end{aligned} $$ In each formula, \(A=\) the child's age, in years, \(D=\) an adult dosage, and \(C=\) the proper child's dosage. The formulas apply for ages 2 through \(13,\) inclusive. Use the formulas to solve Exercises \(93-96\) Use Young's rule to find the difference in a child's dosage for an 8 -year-old child and a 3 -year-old child. Express the answer as a single rational expression in terms of \(D .\) Then describe what your answer means in terms of the variables in the model.

Two formulas that approximate the dosage of a drug prescribed for children are $$ \begin{aligned} \text { Young's rule: } & C=\frac{D A}{A+12} \\ \text { and Cowling's rule: } & C=\frac{D(A+1)}{24} \end{aligned} $$ In each formula, \(A=\) the child's age, in years, \(D=\) an adult dosage, and \(C=\) the proper child's dosage. The formulas apply for ages 2 through \(13,\) inclusive. Use the formulas to solve Exercises \(93-96\) For a 12 -year-old child, what is the difference in the dosage given by Cowling's rule and Young's rule? Express the answer as a single rational expression in terms of \(D\) Then describe what your answer means in terms of the variables in the models.

Factor completely: \(3 x^{2}-15 x-42\) (Section 6.5, Example 2).

Explain how to simplify a rational expression with opposite factors in the numerator and denominator.

Write a rational expression that is undefined for \(x=-4\)

Find the missing rational expression. $$\frac{4}{x-2}+\frac {\text {___}}{\text{___}} =\frac{2 x+8}{{(x-2)}{(x+1)}}$$