Worksheet on Reducing Algebraic Fractions

Practice the questions given in the worksheet on reducing algebraic fractions to its lowest terms. The questions are based on reducing the fractions by cancelling out the common factors in the numerator and denominator.

1. Reduce the following to lowest terms:

(i) \(\frac{a^{2}  -  1}{3a  +  3}\)

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

(iii) \(\frac{a^{2}  -  16}{a^{2}  -  8a  +  16}\)

(iv) \(\frac{5a  -  4}{5a^{2}  -  9a  +  4}\)

(v) \(\frac{8m^{2}n  -  8mn^{2}}{m  +  mn}\)

2. Reduce the rational expression to its lowest terms:

(i) \(\frac{m  -  5}{m^{2}  +  m  -  30}\)

(ii) \(\frac{z^{2}  +  2z  -  24}{z^{2}  -  z -  12}\)

(iii) \(\frac{4d^{2}  +  11d  -  3}{2d^{2}  +  d  -  15}\)

(iv) \(\frac{8a^{2}  +  18a  -  5}{4a^{2}  -  25}\)

(v) \(\frac{m^{2}  -  m  -  6}{m^{2}  +  5m  +  6}\)

(vi) \(\frac{3x^{2}  -  6xy}{2x^{2}y  -  4 xy^{2}}\)

(vii) \(\frac{abz  +  bz^{2}}{acz  +  cz^{2}}\)

(viii) \(\frac{xz}{x^{2}k^{2}  -  xk}\)

(ix) \(\frac{15x^{2}y^{2}z^{2}}{100(x^{2}  -  x^{2}y)}\)

(x) \(\frac{4m^{2}  -  9n^{2}}{4m^{2}  +  6mn}\)

3. Reduce the algebraic fractions to its lowest terms:

(i) \(\frac{20(u^{3}  -  v^{2})}{5u^{2}  +  5uv  +  5v^{2}}\)

(ii) \(\frac{a^{2}  -  5a}{a^{2}  -  4a  -  5}\)

(iii) \(\frac{3m^{2}  +  6m}{m^{2}  +  4m  +  4}\)

(iv) \(\frac{27k  +  k^{4}}{18k  -  6k^{2}  +  2k^{3}}\)

(v) \(\frac{3z^{2}  +  23z  +  14}{3z^{2}  +   41z  +  26}\)

(vi) \(\frac{m^{4}  -  14m^2{2}  -  51}{m^{4}  -  2m^2{2}  -  15}\)

(vii) \(\frac{a^{2}  +  ab  +  2b^{2}}{a^{3}  -  b^{3}}\)

(viii) \(\frac{2a^{2}  +  17a  +  21}{3a^{2}  +  26a  +  35}\)

(ix) \(\frac{x(2a^{2}  -  3ax)}{a(4a^{2}x  -  9x^{3})}\)

(x) \(\frac{(ab  -  3b^{2})^{2}}{a^{2}b^{2}  -  27b^{5}}\)

Answers for the worksheet on reducing algebraic fractions to its lowest terms are given below to check the exact answers of the above simplification.

Answers:

1. (i) \(\frac{a  -  1}{3}\)

(ii) \(\frac{m  -  3}{m  +  3}\)

(iii) \(\frac{a   +  4}{a  -  4}\)

(iv) \(\frac{1}{a  -  1}\)

(v) \(\frac{8n(m  –  n)}{1  +  n}\)

2. (i) \(\frac{1}{m  +  6}\)

(ii) \(\frac{z  +  6}{z  +  3}\)

(iii) \(\frac{4d  -  1}{2d  -  5}\)

(iv) \(\frac{4a  -  1}{2a  -  5}\)

(v) \(\frac{m  -  3}{m  +  3}\)

(vi) \(\frac{3}{2y}\)

(vii) \(\frac{b}{c}\)

(viii) \(\frac{1}{kx  -  1}\)

(ix) \(\frac{3y^{2}z}{20(x  -  y)}\)

(x) \(\frac{2m  -  2n}{2m}\)

3. (i) 4(u - v)

(ii) \(\frac{a}{a  +  1}\)

(iii) \(\frac{3m}{m  +  2}\)

(iv) \(\frac{k  +  3}{2}\)

(v) \(\frac{z  +  7}{z  +  13}\)

(vi) \(\frac{m^{2}  -  17}{m^{2}  -  5}\)

(vii) \(\frac{a  +  2b}{a^{2}  +  ab  +  b^{2}}\)

(viii) \(\frac{2a  +  3}{3a  +  5}\)

(ix) \(\frac{1}{2a  +  3x}\)

(x) \(\frac{a   -  3b}{a^{2}  +  3ab  +  9b^{2}}\)

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