# Worksheet on Algebraic Fractions

Practice the questions given in the worksheet on algebraic fractions. The questions are based on reducing the algebraic fractions to its simplest term.

1. Reducing fractions to its lowest form:

(i) $$\frac{6a + 1}{2} + \frac{7a - 3}{3}$$

(ii) $$n - \frac{n - 1}{2} + \frac{n - 2}{6}$$

(iii) $$\frac{2b - 3}{5b} + \frac{3 - 2b}{15b}$$

(iv) $$\frac{5}{m - 2} + \frac{5}{m + 2}$$

(v) $$\frac{n - 3}{5n} + \frac{n^{2} - 9}{10n^{2}} - \frac{8 - n^{3}}{15n^{3}}$$

(vi) $$\frac{2}{pq} - \frac{3q^{2} - p^{2}}{pq^{3}} + \frac{pq + q^{2}}{p^{2}q^{2}}$$

2. Reduce the following expressions to its simplest form:

(i) $$\frac{x^{2} - 4a^{2}}{ax + 2a^{2}} \times \frac{2a}{x - 2a}$$

(ii) $$\frac{z^{2} - 121}{z^{2} - 4} \div \frac{z + 11}{z + 2}$$

(iii) $$\frac{14k^{2} - 7k}{12k^{3} + 24k^{2}} \div \frac{2k - 1}{k^{2} + 2k}$$

(iv) $$\frac{4m - 1}{3m^{2} - 9m} \div \frac{4m^{2} - m}{m - 3}$$

(v) $$\frac{c^{2} + 4c}{c^{2} + 4c + 3} \div \frac{c^{2} - 16}{c^{2} - 2c - 3}$$

(vi) $$\frac{a^{2} - 25}{9a^{2} - 16b^{2}} \times \frac{3a - 4b}{a^{2} - 5a}$$

3. Simplify algebraic fractions to its lowest terms:

(i) $$\frac{1 + z + z^{2}}{1 - z^{3}} + \frac{z - z^{2}}{(1 - z)^{3}}$$

(ii) $$\frac{2m - 7}{(m - 3)^{2}} - \frac{2(m + 2)}{m^{2} - 9}$$

(iii) $$\frac{2u - 3v}{uv} + \frac{3u - 2k}{ku} + \frac{5}{u}$$

(iv) $$\frac{1}{2k^{2} - \frac{1}{2}} + \frac{1}{(2k + 1)^{2}}$$

(v) $$\frac{1}{(6u - 2)} - \frac{1}{2(u - \frac{1}{3})} - \frac{1}{1 - 3u}$$

Answers for the worksheet on algebraic fractions to its simplest form are given below to check the exact answers of the above simplification.

1. (i) $$\frac{32a - 3}{6}$$

(ii) $$\frac{4n + 1}{6}$$

(iii) $$\frac{4b - 6}{15b}$$

(iv) $$\frac{10m}{(m + 2) (m – 2)}$$

(v) $$\frac{11n^{3} – 18n^{2} – 27n - 16}{30n^{3}}$$

(vi) $$\frac{p^{3} + q^{3}}{p^{2}q^{3}}$$

2. (i) 2

(ii) $$\frac{z - 11}{z - 2}$$

(iii) $$\frac{7}{12}$$

(iv) $$\frac{1}{3m^{ 2}}$$

(v) $$\frac{c(c – 3)}{(c + 3) (c – 4)}$$

(vi) $$\frac{a + 5}{a(3a + 4b)}$$

3. (i) $$\frac{1}{(1 - z)^{2}}$$

(ii) $$\frac{m - 9}{(m^{2} – 9) (m - 3)}$$

(iii) $$\frac{3v + 2k}{kv}$$

(iv) $$\frac{6k + 1}{(2k + 1)^{2} (2k – 1)}$$

(v) 0

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