Everything Maths Grade 10

Step 3: Cancel the common factor in the numerator and the denominator to give the final answer

=

a+ 1

ax

Worked example 19: Simplifying fractions

QUESTION

Simplify:
x^2 x 2
x^2 4



x^2 +x

x^2 + 2x

; (x̸= 0;x̸=±2)

SOLUTION

Step 1: Factorise the numerator and denominator

=

(x+ 1) (x2)

(x+ 2) (x2)



x(x+ 1)

x(x+ 2)

Step 2: Change the division sign and multiply by the reciprocal

=

(x+ 1) (x2)

(x+ 2) (x2)



x(x+ 2)

x(x+ 1)

Step 3: Write the final answer

= 1

Worked example 20: Simplifying fractions

QUESTION

Simplify:
x 2
x^2 4

+

x^2

x 2

x^3 +x 4

x^2  4

; (x̸=±2)

SOLUTION

Step 1: Factorise the denominators

x 2

(x+ 2) (x2)

+

x^2

x 2

x^3 +x 4

(x+ 2) (x2)

32 1.8. Simplification of fractions