Topic/Skill Definition/Tips
Topic: Algebraic Fractions Example
1. Algebraic A fraction whose numerator and 6x
Fraction denominator are algebraic expressions. 3 x −1
2. Adding/ a c 1 x
For ± , the common denominator is +
Subtracting b d x 2y
Algebraic bd 1(2 y ) x ( x )
Fractions ¿ +
2 xy 2 xy
a c ad bc ad ± bc 2 y+x
2
± = ± = ¿
b d bd bd bd
2 xy
3. Multiplying Multiply the numerators together and the x x+2
×
Algebraic denominators together. 3 x −2
Fractions x ( x+ 2 )
a c ac ¿
× = 3 ( x−2 )
b d bd 2
x +2 x
¿
3 x−6
4. Dividing Multiply the first fraction by the x 2x
÷
Algebraic reciprocal of the second fraction. 3 7
Fractions x 7
a c a d ad ¿ ×
÷ = × = 3 2x
b d b c bc 7x 7
¿ =
6x 6
5. Simplifying Factorise the numerator and denominator 2
x + x−6 ( x+ 3)( x −2) x+ 3
Algebraic and cancel common factors. = =
2 x−4 2(x−2) 2
Fractions
Mr A. Coleman Glyn School
Topic: Algebraic Fractions Example
1. Algebraic A fraction whose numerator and 6x
Fraction denominator are algebraic expressions. 3 x −1
2. Adding/ a c 1 x
For ± , the common denominator is +
Subtracting b d x 2y
Algebraic bd 1(2 y ) x ( x )
Fractions ¿ +
2 xy 2 xy
a c ad bc ad ± bc 2 y+x
2
± = ± = ¿
b d bd bd bd
2 xy
3. Multiplying Multiply the numerators together and the x x+2
×
Algebraic denominators together. 3 x −2
Fractions x ( x+ 2 )
a c ac ¿
× = 3 ( x−2 )
b d bd 2
x +2 x
¿
3 x−6
4. Dividing Multiply the first fraction by the x 2x
÷
Algebraic reciprocal of the second fraction. 3 7
Fractions x 7
a c a d ad ¿ ×
÷ = × = 3 2x
b d b c bc 7x 7
¿ =
6x 6
5. Simplifying Factorise the numerator and denominator 2
x + x−6 ( x+ 3)( x −2) x+ 3
Algebraic and cancel common factors. = =
2 x−4 2(x−2) 2
Fractions
Mr A. Coleman Glyn School
