Everything Maths Grade 10

Step 2: Make all denominators the same so that we can add or subtract the fractions

The lowest common denominator is(x2) (x+ 2).

x 2

(x+ 2) (x2)

+

(

x^2

)

(x+ 2)

(x+ 2) (x2)

x^3 +x 4

(x+ 2) (x2)

Step 3: Write as one fraction

x2 +

(

x^2

)

(x+ 2)

(

x^3 +x 4

)

(x+ 2) (x2)

Step 4: Simplify

x2 +x^3 + 2x^2 x^3 x+ 4

(x+ 2) (x2)

=

2 x^2 + 2

(x+ 2) (x2)

Step 5: Take out the common factor and write the final answer

2

(

x^2 + 1

)

(x+ 2) (x2)

Worked example 21: Simplifying fractions

QUESTION

Simplify:
2
x^2 x

+

x^2 +x+ 1

x^3  1

x

x^2  1

; (x̸= 0;x̸=±1)

SOLUTION

Step 1: Factorise the numerator and denominator

2

x(x1)

+

(

x^2 +x+ 1

)

(x1) (x^2 +x+ 1)

x

(x1) (x+ 1)

Step 2: Simplify and find the common denominator

2 (x+ 1) +x(x+ 1)x^2

x(x1) (x+ 1)

Step 3: Write the final answer

2 x+ 2 +x^2 +xx^2

x(x1) (x+ 1)

=

3 x+ 2

x(x1) (x+ 1)

Chapter 1. Algebraic expressions 33