Chapter 11

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(\frac{3 x}{5}+7 x=38\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{3}{5}-\frac{1}{3}$$

Simplify. Leave your answers as improper fractions. $$\frac{\frac{a}{b}+\frac{x}{y}}{\frac{a}{z}-\frac{x}{c}}$$

Factor completely.$$16 x^{2}-16 y^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$c^{2}+9 c+18$$

Simplify each fraction by manipulating the algebraic signs. $$-\frac{2 x-y}{y-2 x}$$

Multiply and reduce. Do some by calculator. $$3 \times \frac{5}{8} \times \frac{4}{5}$$

Solve for \(x .\) Try some by calculator. $$\frac{a}{2}(x-3 w)=z$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(\frac{x}{2}+\frac{x}{3}+\frac{x}{4}=26\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{3}{4}+\frac{7}{16}$$

Simplify. Leave your answers as improper fractions. $$\frac{1+\frac{x}{y}}{1-\frac{x^{2}}{y^{2}}}$$

Factor completely.$$9 c^{2}-16 d^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}-4 x-21$$

Simplify each fraction by manipulating the algebraic signs. $$\frac{(a-b)(c-d)}{b-a}$$

Multiply and reduce. Do some by calculator. $$\frac{15 a^{2}}{7 b^{2}} \cdot \frac{28 a b}{9 a^{3} c}$$

Solve for \(x .\) Try some by calculator. $$c x-x=b c-b$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(\frac{x-1}{2}=\frac{x+1}{3}\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{2}{3}+\frac{3}{7}$$

Factor completely.$$25 a^{2}-9 b^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}-x-56$$

Simplify each fraction by manipulating the algebraic signs. $$\frac{w(x-y-z)}{y-x+z}$$

$$\frac{3 a b^{2}}{y^{3}}-\frac{6 a^{2} b}{y^{2}}+\frac{12 a b}{y}$$

Multiply and reduce. Do some by calculator. $$\frac{a^{4} b^{4}}{2 a^{2} y^{n}} \cdot \frac{a^{2} x}{x y^{n}}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(\frac{3 x-1}{4}=\frac{2 x+1}{3}\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{5}{9}-\frac{1}{3}+\frac{3}{18}$$

Simplify. Leave your answers as improper fractions. $$\frac{a^{2}+\frac{x}{3}}{4+\frac{x}{5}}$$

Factor completely.$$9 y^{2}-1$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}+6 x+8$$

Reduce to lowest terms. Write your answers without negative exponents. Do some algebraic fractions by calculator. $$\frac{14}{21}$$

$$\frac{5 m}{2 n}+\frac{15 m^{2}}{4 n^{2}}-\frac{25 m^{3}}{8 n}$$

Multiply and reduce. Do some by calculator. $$\frac{x+y}{x-y} \cdot \frac{x^{2}-y^{2}}{(x+y)^{2}}$$

Solve for \(x .\) Try some by calculator. $$a x+m=c x+n$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(x+\frac{2 x}{3}+\frac{3 x}{4}=29\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$\frac{1}{2}+\frac{1}{3}+\frac{1}{5}$$

Simplify. Leave your answers as improper fractions. $$\frac{3 a^{2}-3 y^{2}}{\frac{a+y}{3}}$$

Factor completely.$$4 x^{2}-9 y^{2}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$x^{2}+12 x+32$$

Reduce to lowest terms. Write your answers without negative exponents. Do some algebraic fractions by calculator. $$\frac{81}{18}$$

$$\frac{16 y^{2}}{9 x^{2}}-\frac{8 y^{3}}{3 x^{3}}+\frac{24 y^{4}}{9 x}$$

Multiply and reduce. Do some by calculator. $$\frac{x^{2}-a^{2}}{x y} \cdot \frac{x y}{x+a}$$

Solve for \(x .\) Try some by calculator. $$a x-b x=c+d x-m$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(2 x+\frac{x}{3}-\frac{x}{4}=50\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$2+\frac{3}{5}$$

Challenge Problems.$$m^{4}-n^{4}$$

Factor completely, by hand or by calculator. Check your results. Trinomials with a Leading Coefficient of 1. $$b^{2}-8 b+15$$

Reduce to lowest terms. Write your answers without negative exponents. Do some algebraic fractions by calculator. $$\frac{75}{35}$$

$$5 a^{2} b+6 a^{2} c$$

Multiply and reduce. Do some by calculator. $$\frac{a}{x-y} \cdot \frac{b}{x+y}$$

Solve for \(x\). Assume the integers in these equations to be exact numbers, and leave your answers in fractional form. \(3 x-\frac{2 x}{3}-\frac{5 x}{6}=18\)

Combine and simplify. Don't use your calculator for these numerical problems. The practice you get working with common fractions will help you when doing algebraic fractions. $$3-\frac{2}{3}+\frac{1}{6}$$