91Ó°ÊÓ

Solve each problem. In a certain fraction, the denominator is 6 more than the numerator. If 3 is added to both the numerator and the denominator, the resulting fraction is equivalent to \(\frac{5}{7} .\) What was the original fraction (not written in lowest terms)?

Multiply. Write each answer in lowest terms. See Examples I and 2. $$\frac{2(c+d)}{3} \cdot \frac{18}{6(c+d)^{2}}$$

Determine whether each equation represents direct or inverse variation. $$ y=\frac{3}{x} $$

Add or subtract. Write answer in lowest terms. \(\frac{5}{p}+\frac{12}{p}\)

Find the LCD for the fractions in each list. $$ \frac{12}{m^{7}}, \frac{14}{m^{8}} $$

Determine whether each equation represents direct or inverse variation. $$ y=50 x $$

Determine whether each equation represents direct or inverse variation. $$ y=200 x $$

Why can't the denominator of a rational expression equal \(0 ?\)

When solving an equation with variables in denominators, we must determine the values thar cause these denominators to equal 0, so that we can reject these extraneous values if they= appear as potential solutions. Find all values for which at least one denominator is equal to \(0 .\) Write answers using the symbol \(\neq\) Do not solve. See Examples \(3-7\). $$ \frac{4}{x^{2}+8 x-9}+\frac{1}{x^{2}-4}=0 $$

Fill in each blank with the correct response. (a) If the constant of variation is positive and \(y\) varies directly as \(x,\) then as \(x\) increases, \(y=\) ____. (increases/decreases) (b) If the constant of variation is positive and \(y\) varies inversely as \(x,\) then as \(x\) increases, \(V\) ____. (increases/decreases)