Chapter 7

For exercises \(25-68\), evaluate or simplify. $$ \frac{\frac{2}{x-2}+\frac{3}{x+3}}{\frac{2}{x-2}+\frac{1}{x+3}} $$

For exercises \(5-48\), simplify. $$ \frac{8 p^{2}}{4 p^{2}+32 p+64}-\frac{128}{4 p^{2}+32 p+64} $$

For exercises 39-82, simplify. $$ \frac{4 c}{7} \div \frac{8}{21 c^{2}} $$

For exercises 1-66, simplify. $$ \frac{p^{2}-6 p-27}{p^{2}-2 p-15} $$

For exercises \(45-48\), the formula \(R=\frac{U F}{P}\) describes the glomular filtration rate by a kidney \(R\). Is the relationship of the given variables a direct variation or an inverse variation? $$ F \text { and } P \text { are constant; the relationship of } R \text { and } U \text {. } $$

For exercises \(25-68\), evaluate or simplify. $$ \frac{\frac{1}{x+3}+\frac{2}{x-2}}{\frac{2}{x+3}-\frac{3}{x-2}} $$

For exercises \(5-48\), simplify. $$ \frac{3 y^{2}}{5 y^{2}+60 y+180}-\frac{12 y+180}{5 y^{2}+60 y+180} $$

For exercises 39-82, simplify. $$ \frac{a}{3 b} \div \frac{a}{6 c} $$

For exercises 1-66, simplify. $$ \frac{x^{2}-4 x+3}{x^{2}-3 x+2} $$

For exercises \(45-48\), the formula \(R=\frac{U F}{P}\) describes the glomular filtration rate by a kidney \(R\). Is the relationship of the given variables a direct variation or an inverse variation? $$ U \text { and } P \text { are constant; the relationship of } R \text { and } F \text {. } $$

For exercises \(25-68\), evaluate or simplify. $$ \frac{\frac{3}{x-4}-\frac{1}{x+2}}{\frac{6}{x-4}+\frac{5}{x+2}} $$

For exercises \(5-48\), simplify. $$ \frac{2 x^{2}}{3 x^{2}+24 x+48}-\frac{8 x+64}{3 x^{2}+24 x+48} $$

For exercises 39-82, simplify. $$ \frac{h}{5 k} \div \frac{h}{10 m} $$

For exercises \(45-48\), the formula \(R=\frac{U F}{P}\) describes the glomular filtration rate by a kidney \(R\). Is the relationship of the given variables a direct variation or an inverse variation? $$ U \text { and } F \text { are constant; the relationship of } R \text { and } P \text {. } $$

For exercises \(25-68\), evaluate or simplify. $$ \frac{\frac{1}{x+3}+\frac{2}{x-2}}{\frac{2}{x+3}-\frac{3}{x-2}} $$

For exercises \(5-48\), simplify. $$ \frac{2 v^{2}}{2 v^{2}+5 v-12}+\frac{13 v}{2 v^{2}+5 v-12}-\frac{24}{2 v^{2}+5 v-12} $$

For exercises 39-82, simplify. $$ \frac{8 a b}{21 c^{2}} \div \frac{2 a^{2}}{3 c} $$

For exercises 1-66, simplify. $$ \frac{y^{2}+11 y+28}{y^{2}-2 y-63} $$

For exercises \(45-48\), the formula \(R=\frac{U F}{P}\) describes the glomular filtration rate by a kidney \(R\). Is the relationship of the given variables a direct variation or an inverse variation? $$ R \text { and } P \text { are constant; the relationship of } U \text { and } F \text {. } $$

For exercises 43-58, (a) solve. (b) check. $$ \frac{4}{a+6}=\frac{9}{a-4} $$

For exercises \(25-68\), evaluate or simplify. $$ \frac{\frac{3}{x+1}+\frac{1}{x-2}}{\frac{1}{x+1}-\frac{4}{x-2}} $$

For exercises 39-82, simplify. $$ \frac{9 h k}{40 n^{2}} \div \frac{3 h^{2}}{8 n} $$

For exercises 1-66, simplify. $$ \frac{y^{2}+11 y+30}{y^{2}-2 y-48} $$

For exercises 49-52, the formula \(C=\frac{P_{m} P_{i}}{T F}\) describes the cost of insurance, \(C\). Is the relationship of the given variables a direct variation or an inverse variation? $$ P_{i}, T \text {, and } F \text { are constant; the relationship of } C \text { and } P_{m} \text {. } $$

For exercises 43-58, (a) solve. (b) check. $$ \frac{9}{10} v+\frac{1}{3}=-\frac{22}{15} $$

For exercises \(25-68\), evaluate or simplify. $$ \frac{\frac{1}{x-4}-2}{\frac{4}{x+5}-4} $$

For exercises 49-52, simplify. $$ \frac{n^{3}}{n^{2}+n-12}-\frac{27}{n^{2}+n-12} $$

For exercises 39-82, simplify. $$ \frac{9 x^{2}}{8 y} \div \frac{x}{y} $$

For exercises 1-66, simplify. $$ \frac{6 x^{3}+18 x^{2}+12 x}{9 x^{2}+9 x-18} $$

For exercises 49-52, the formula \(C=\frac{P_{m} P_{i}}{T F}\) describes the cost of insurance, \(C\). Is the relationship of the given variables a direct variation or an inverse variation? $$ P_{m}, T \text {, and } F \text { are constant; the relationship of } C \text { and } P_{i} $$

For exercises 49-52, simplify. $$ \frac{z^{3}}{z^{2}+5 z-14}-\frac{8}{z^{2}+5 z-14} $$

For exercises 39-82, simplify. $$ \frac{15 a^{2}}{14 d} \div \frac{a}{d} $$

For exercises 49-52, the formula \(C=\frac{P_{m} P_{i}}{T F}\) describes the cost of insurance, \(C\). Is the relationship of the given variables a direct variation or an inverse variation? $$ C, T, \text { and } F \text { are constant; the relationship of } P_{i} \text { and } P_{m} $$

For exercises \(25-68\), evaluate or simplify. $$ \frac{5-\frac{1}{x+3}}{2+\frac{4}{x-1}} $$

For exercises 49-52, simplify. $$ \frac{k^{3}}{k^{2}+14 k+40}+\frac{64}{k^{2}+14 k+40} $$

For exercises 39-82, simplify. $$ \frac{3 b}{8 d} \div \frac{3 b}{20 d} $$

For exercises 1-66, simplify. $$ \frac{2 c^{2}-13 c-45}{2 c^{2}+13 c+20} $$

For exercises \(35-86\), simplify. $$ \frac{v+1}{6 v-24}-\frac{v}{v-4} $$

For exercises 49-52, simplify. $$ \frac{m^{3}}{m^{2}+12 m+27}+\frac{27}{m^{2}+12 m+27} $$

For exercises 39-82, simplify. $$ \frac{7 w}{9 p} \div \frac{7 w}{30 p} $$

For exercises 1-66, simplify. $$ \frac{2 w^{2}+9 w+7}{2 w^{2}+13 w+21} $$

For exercises 53-56, the formula \(F=\frac{100 S_{u} C_{p}}{S_{p} C_{u}}\) describes the fractional excretion of sodium, \(F\). Is the relationship of the given variables a direct variation or an inverse variation? $$ S_{u}, S_{p} \text {, and } C_{u} \text { are constant; the relationship of } F \text { and } C_{p} \text {. } $$

For exercises 43-58, (a) solve. (b) check. $$ \frac{2}{x}=0 $$

For exercises 1-66, simplify. $$ \frac{9 n^{2}-48 n+64}{9 n^{2}-64} $$

For exercises 53-56, the formula \(F=\frac{100 S_{u} C_{p}}{S_{p} C_{u}}\) describes the fractional excretion of sodium, \(F\). Is the relationship of the given variables a direct variation or an inverse variation? $$ C_{p}, S_{p} \text {, and } C_{u} \text { are constant; the relationship of } F \text { and } S_{u} $$

For exercises \(25-68\), evaluate or simplify. $$ \frac{\frac{x}{x-2}}{\frac{x+4}{x+3}} $$

For exercises \(35-86\), simplify. $$ \frac{4}{z^{2}+3 z}+\frac{5}{z^{2}+9 z} $$

A student is simplifying \(\frac{x+3}{x+4}\). He thinks that the \(x\) in the numerator and the \(x\) in the denominator are common factors and that the expression will simplify to \(\frac{3}{4}\). Explain why he cannot simplify the expression in this way.

For exercises 39-82, simplify. $$ \frac{5 x-20}{4} \div \frac{5}{2} $$

For exercises 1-66, simplify. $$ \frac{9 p^{2}-30 p+25}{9 p^{2}-25} $$