Worksheet on Simplifying Algebraic Fractions

Practice the simplification provided in the worksheet on simplifying algebraic fractions. The questions are based on simplifying the expressions by cancelling out the common factor from both the numerator and denominator and then simplify by adding or subtracting or multiplying if required.

1. Simplify by adding and subtracting algebraic fractions:

(i) \(\frac{p}{p  -  2} - \frac{p^{2}}{p^{2}  -  4}\)

(ii) \(\frac{3}{a  -  b} - \frac{1}{a  +  b} + \frac{4b}{a^{2}  -  b^{2}}\)

(iii) \(\frac{3}{m  -  3} + \frac{5}{3m  -  9}\)

(iv) \(\frac{z  -  1}{2} + \frac{z  +  3}{5} + \frac{z  +  7}{10}\)

(v) \(\frac{2z  -  1}{3} + \frac{z  -  5}{6} + \frac{z  -  4}{4}\)

(vi) \(\frac{5z  -  1}{8} - \frac{3z  -  2}{7} + \frac{z  -  5}{4}\)

2. Simplify by multiplying and dividing algebraic fractions:

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

(ii) \(\frac{z^{2}  -  25}{z^{2}  -  4} \times \frac{z  -  2}{z  +  5}\)

(iii) \(\frac{u^{2}  -  16}{u^{2}  -  49} \times \frac{u  +  7}{u  +  4}\)

(iv) \(\frac{m^{2}n^{2}  +  3mn}{4m^{2}  -  1} \div \frac{mn  +  3}{2m  +  1}\)

(v) \(\frac{p^{2}  -  p  -  12}{5p} \times \frac{p^{3}  -  p}{p^{2}  -  9 }\)

(vi) \(\frac{a  +  b}{2a  -  3} \times \frac{a  -  b}{2a  +  3}\)


3. Simplify by cancelling algebraic fractions:

(i) \(\frac{k  -  m}{m} + \frac{k  +  m}{m} - \frac{k^{2}  -  m^{2}}{2km}\)

(ii) \(\frac{z  +  2}{17z} - \frac{z  -  5}{34z} + \frac{z  +  2}{51z}\)

(iii) \(\frac{2x^{2}  -  y^{2}}{x^{2}} - \frac{y^{2}  -  z^{2}}{y^{2}} - \frac{z^{2}  -  x^{2}}{z^{2}}\)

(iv) \(\frac{(d  +  1)^{3}  -  (d  -  1)^{3}}{3d^{3}  +  d}\)

(v) \(\frac{1}{(1  -  a)^{2}} + \frac{2}{1  -  a^{2}} + \frac{1}{(1  +  a)^{2}}\)

(vi) \(\frac{(m^{3}  -  2m)^{2}  -  (m^{2}  -  2)^{2}}{(m  -  1)(m  +  1)(m^{2}  -  2)}\)


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

Answers:


1. (i) \(\frac{2p}{(p  +  2) (p  –  2)}\)

(ii) \(\frac{2(a  +  4b)}{(a  +  b) (a  –  b)}\)

(iii) \(\frac{14}{3(m  -  3}\)

(iv) \(\frac{4(z  +  1)}{5}\)

(v) \(\frac{13(z  –  2)}{12}\)

(vi) \(\frac{25z  -  61}{56}\)


2. (i) 2

(ii) \(\frac{z  -  5}{z  +  2}\)

(iii) \(\frac{u  -  4}{u  -  7}\)

(iv) \(\frac{mn}{2m  -  1}\)

(v) \(\frac{(p  –  4) (p^{2}  –  1)}{5(p  –  3)}\)

(vi) \(\frac{a^{2}  –  b^{2}}{4a^{2}  -  9}\)


3. (i) \(\frac{k^{2}  +  3m^{2}}{2km}\)

(ii) \(\frac{5z  +  31}{102z}\)

(iii) \(\frac{x^{4}y^{2}  –  y^{4}z^{2}  +  x^{2}z^{4} }{x^{2}y^{2}z^{2}}\)

(iv) \(\frac{2}{d}\)

(v) \(\frac{4}{(1  -  a^{2})^{2}}\)

(vi) 1






Math Homework Sheets

8th Grade Math Practice

From Worksheet on Simplifying Algebraic Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Jul 12, 24 03:08 PM

    Fractions
    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Worksheet on Fractions | Questions on Fractions | Representation | Ans

    Jul 12, 24 02:11 PM

    Worksheet on Fractions
    In worksheet on fractions, all grade students can practice the questions on fractions on a whole number and also on representation of a fraction. This exercise sheet on fractions can be practiced

    Read More

  3. Fraction in Lowest Terms |Reducing Fractions|Fraction in Simplest Form

    Jul 12, 24 03:21 AM

    Fraction 8/16
    There are two methods to reduce a given fraction to its simplest form, viz., H.C.F. Method and Prime Factorization Method. If numerator and denominator of a fraction have no common factor other than 1…

    Read More

  4. Conversion of Improper Fractions into Mixed Fractions |Solved Examples

    Jul 12, 24 12:59 AM

    To convert an improper fraction into a mixed number, divide the numerator of the given improper fraction by its denominator. The quotient will represent the whole number and the remainder so obtained…

    Read More

  5. Conversion of Mixed Fractions into Improper Fractions |Solved Examples

    Jul 12, 24 12:30 AM

    Conversion of Mixed Fractions into Improper Fractions
    To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the proper fraction and then to the product add the numerator of the fraction to get the numerat…

    Read More