8.3 Add and Subtract Rational Expressions with a Common Denominator

If you miss a problem, go back to the section listed and review the material.

Add: $\frac{y}{3} + \frac{9}{3} .$
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Subtract: $\frac{10}{x} - \frac{2}{x} .$
If you missed this problem, review the reference.

Factor completely: $45 a^{3} - 5 a b^{2} .$
If you missed this problem, review the reference.

Add: $\frac{5}{18} + \frac{7}{18} .$

Add: $\frac{7}{16} + \frac{5}{16} .$

Add: $\frac{3}{10} + \frac{1}{10} .$

Add: $\frac{3 y}{4 y - 3} + \frac{7}{4 y - 3} .$

Add: $\frac{5 x}{2 x + 3} + \frac{2}{2 x + 3} .$

Add: $\frac{x}{x - 2} + \frac{1}{x - 2} .$

Add: $\frac{7 x + 12}{x + 3} + \frac{x^{2}}{x + 3} .$

Add: $\frac{9 x + 14}{x + 7} + \frac{x^{2}}{x + 7} .$

Add: $\frac{x^{2} + 8 x}{x + 5} + \frac{15}{x + 5} .$

Subtract: $\frac{n^{2}}{n - 10} - \frac{100}{n - 10} .$

Subtract: $\frac{x^{2}}{x + 3} - \frac{9}{x + 3} .$

Subtract: $\frac{4 x^{2}}{2 x - 5} - \frac{25}{2 x - 5} .$

Subtract: $\frac{y^{2}}{y - 6} - \frac{2 y + 24}{y - 6} .$

Subtract: $\frac{n^{2}}{n - 4} - \frac{n + 12}{n - 4} .$

Subtract: $\frac{y^{2}}{y - 1} - \frac{9 y - 8}{y - 1} .$

Subtract: $\frac{5 x^{2} - 7 x + 3}{x^{2} - 3 x – 18} - \frac{4 x^{2} + x - 9}{x^{2} - 3 x – 18} .$

Subtract: $\frac{4 x^{2} - 11 x + 8}{x^{2} - 3 x + 2} - \frac{3 x^{2} + x - 3}{x^{2} - 3 x + 2} .$

Subtract: $\frac{6 x^{2} - x + 20}{x^{2} - 81} - \frac{5 x^{2} + 11 x - 7}{x^{2} - 81} .$

Add: $\frac{8 x - 15}{2 x - 5} + \frac{2 x}{5 - 2 x} .$

Add: $\frac{6 y^{2} + 7 y - 10}{4 y - 7} + \frac{2 y^{2} + 2 y + 11}{7 - 4 y} .$

Subtract: $\frac{y^{2} - 5 y}{y^{2} - 4} - \frac{6 y - 6}{4 - y^{2}} .$

Subtract: $\frac{2 n^{2} + 8 n - 1}{n^{2} - 1} - \frac{n^{2} - 7 n - 1}{1 - n^{2}} .$

Add.

$\frac{2}{15} + \frac{7}{15}$

Add.

$\frac{7}{24} + \frac{11}{24}$

Add.

$\frac{3 a}{a - b} + \frac{1}{a - b}$

Add.

$\frac{d}{d + 8} + \frac{5}{d + 8}$

Add.

$\frac{p^{2} + 10 p}{p + 2} + \frac{16}{p + 2}$

Add.

$\frac{2 r^{2}}{2 r - 1} + \frac{15 r - 8}{2 r - 1}$

Add.

$\frac{8 t^{2}}{t + 4} + \frac{32 t}{t + 4}$

Add.

$\frac{2 w^{2}}{w^{2} - 16} + \frac{8 w}{w^{2} - 16}$

Subtract.

$\frac{y^{2}}{y + 8} - \frac{64}{y + 8}$

Subtract.

$\frac{9 a^{2}}{3 a - 7} - \frac{49}{3 a - 7}$

Subtract.

$\frac{c^{2}}{c - 8} - \frac{6 c + 16}{c - 8}$

Subtract.

$\frac{3 m^{2}}{6 m - 30} - \frac{21 m - 30}{6 m - 30}$

Subtract.

$\frac{6 p^{2} + 3 p + 4}{p^{2} + 4 p - 5} - \frac{5 p^{2} + p + 7}{p^{2} + 4 p - 5}$

Subtract.

$\frac{5 r^{2} + 7 r - 33}{r^{2} - 49} - \frac{4 r^{2} + 5 r + 30}{r^{2} - 49}$

Add.

$\frac{10 v}{2 v - 1} + \frac{2 v + 4}{1 - 2 v}$

Add.

$\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x}$

Subtract.

$\frac{z^{2} + 6 z}{z^{2} - 25} - \frac{3 z + 20}{25 - z^{2}}$

Subtract.

$\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}}$

Sarah ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. If $r$ represents Sarah’s speed when she ran, then her running time is modeled by the expression $\frac{8}{r}$ and her biking time is modeled by the expression $\frac{24}{r + 4} .$ Add the rational expressions $\frac{8}{r} + \frac{24}{r + 4}$ to get an expression for the total amount of time Sarah ran and biked.